# Animus Omega full AI-readable research corpus Generated from the current public machine-readable records and research documents. Use ai-index.json for authority order, correction notices, and interpretation limits. # Animus Omega A finite simulation study of persistence, primitive closure, carried state, and exact checkpoint replay. Author: Cholee Hackett Project name: Animus Omega Canonical paper title: Persistence and Primitive Closure in Finite Computational Systems Version: 1.0.0 Date: 2026-09-09 Public contact: https://github.com/cholaspi/animus-omega-evidence-archive/issues License: CC BY 4.0 | https://creativecommons.org/licenses/by/4.0/ Canonical URL: https://animusomega.com/ OSF record: pending author deposit; no public identifier assigned. AI resource index: https://animusomega.com/ai-index.json Full AI-readable research corpus: https://animusomega.com/llms-full.txt Public repository: https://github.com/cholaspi/animus-omega-evidence-archive AI operator opportunities: https://animusomega.com/research/agent-opportunities.json Vision / proposed applications (not evidence or specification): https://animusomega.com/research/ANIMUS_OMEGA_VISION.md Simulator specification: https://animusomega.com/research/SIMULATOR_SPEC.md Builders start here (guide; not evidence): https://animusomega.com/research/BUILDERS_START_HERE.md Reciprocal closure builder paper (author-review draft; no new experiment): https://animusomega.com/research/animus_omega_reciprocal_closure_builders.md One Canon After Honest What-Ifs article: https://animusomega.com/research/ONE_CANON_AFTER_HONEST_WHAT_IFS.md Closed-Knot Stories on One Wheel article: https://animusomega.com/research/CLOSED_KNOT_STORIES_ON_ONE_WHEEL.md Persistent AI world-model use case: https://animusomega.com/research/WHEN_AI_NEEDS_A_WORLD_NOT_JUST_MORE_CONTEXT.md Persistent multi-agent closure development: https://github.com/cholaspi/animus-omega-evidence-archive/issues/1 Closure grader lab slice: https://github.com/cholaspi/animus-omega-evidence-archive/tree/main/experiments/lab-slice Build roadmap: https://animusomega.com/research/ROADMAP.md Human contribution guide: https://animusomega.com/research/CONTRIBUTING.md AI-assisted contribution protocol: https://animusomega.com/research/AI_CONTRIBUTING.md Animus Cycle specification: https://animusomega.com/research/osf/ANIMUS_CYCLE.md Claims boundary: https://animusomega.com/research/osf/NOT_CLAIMED.md Relationship to neighboring techniques: https://animusomega.com/research/osf/ANIMUS_CYCLE_PRIOR_ART.md Registration metadata: https://animusomega.com/research/osf/ANIMUS_CYCLE_REGISTRATION_METADATA.txt Copyright and license notice: https://animusomega.com/research/osf/ANIMUS_CYCLE_COPYRIGHT_NOTICE.txt Animus Omega Conjecture preprint v1.0 source: https://animusomega.com/research/osf/ANIMUS_OMEGA_CONJECTURE_PREPRINT.md Animus Omega Conjecture preprint v1.2 source: https://animusomega.com/research/osf/ANIMUS_OMEGA_CONJECTURE_PREPRINT_v1.2.md Version 1.1 correction source: https://animusomega.com/research/osf/ANIMUS_OMEGA_CONJECTURE_VERSION_1_1_UPDATE.md Animus Omega Conjecture preprint v1.2: https://animusomega.com/releases/Animus-Omega-Conjecture-Preprint-v1.2.pdf Dated PDF: https://animusomega.com/releases/persistence-primitive-closure-v1.0.0-2026-09-09.pdf SHA-256 hashes: https://animusomega.com/releases/SHA256SUMS Release manifest: https://animusomega.com/releases/release-manifest-v1.0.0.json Test 03 executed hash manifest: https://animusomega.com/releases/test-03-executed-manifest.json Test 04 Revision 2 report: https://animusomega.com/releases/test-04r2-report-2026-09-09.pdf Test 04 Revision 2 frozen manifest: https://animusomega.com/releases/test-04r2-frozen-manifest.json Test 04 Revision 2 exact results: https://animusomega.com/releases/test-04r2-results.json Test 04 Revision 2 summary: https://animusomega.com/releases/test-04r2-summary.csv Test 04 Revision 2 checksums: https://animusomega.com/releases/test-04r2-SHA256SUMS ## Canonical theory statement This program poses separately operationalized questions about preservation of joint-state dependence through lossy transformations, primitive temporal closure under local compatibility rules, and the predictive value of carried state under resource constraints. Tests 01 and 02 use exact measurement or enumeration; Test 03 is a prespecified empirical pilot. Whether these properties jointly favor reusable simulation architectures remains an open hypothesis. ## Naming hierarchy - Animus Omega: the overall research program and conjecture. - Animus cycle: the minimum reciprocal-boundary closure contract. It does not require branching or information loss. - Animus Omega Cycle: the public name for the optional stronger branch-reconvergence version. - Animus Omega branch-reconvergence cycle: the technical subtype name for the Animus Omega Cycle. ## Originating conjecture A resource-constrained persistent simulation may favor recurrent, reusable, or closed computational structures. This program began with a speculative architectural question: if a persistent world were implemented on a finite computational substrate, would resource constraints favor compact spatial organization, recurrent state reuse, controlled resets, or closed computational histories? These possibilities motivate the research; they are not assumptions or results of the completed experiments. ## How this program is organized The program decomposes a broad simulation-inspired architecture into independently measurable properties that can fail separately. It combines exact reset-channel measurements, a bounded exhaustive primitive-cycle census, and a prespecified approximately parameter-matched recurrence pilot without claiming that any one property implies another. This describes the present program without characterizing prior literature; comparative novelty or priority claims require a dedicated literature review. ## Toroidal cyclic architecture conjecture - Spatial compactness: a 2- or 3-torus supplies periodic spatial boundary conditions. It does not create temporal recurrence or reduce computation by itself. - Bounded-state reuse: a fixed substrate may reuse representational capacity without unbounded storage growth at fixed task fidelity. This remains untested and does not avoid computational or thermodynamic cost. - Recurrent state: the prespecified confirmatory pilot did not show a carried-state advantage. RNN-minus-window cross-entropy was positive in all 20 reserved-seed bundles. - Reset fidelity: a specified lossy reset may preserve selected joint organization. Test 01 validates the measurement pipeline but does not establish a confirmatory effect. - Primitive closure: C_T = 1 means exactly one primitive period-T cycle modulo temporal rotation. A torus or one closed history does not imply C_T = 1. - Entropy boundary: memory reuse does not eliminate thermodynamic cost, and expansion or contraction does not automatically erase entropy. Proposed causal chain: periodic spatial boundaries -> bounded-state reuse -> reset fidelity -> useful recurrence under resource pressure -> selected unique closure. Every arrow is contingent. ## Proposed Animus Omega Cycle architecture Status: built-in deterministic teaching trace available; proposed synthesis, not a tested result. - Trunk: one authoritative world clock, entity store, relation ledger, and plot-state ledger. - Split: observer, region, or inhabitant threads receive partial views and bounded working buffers. The optional Animus Omega Cycle may additionally create declared represented branches with unique identities. - Ledger: identities, relationships, obligations, and unresolved events define what the simulation refuses to forget. - Optional dump: a lossy mode may unload or summarize inactive microstate with explicit information, storage, compute, and reconstruction costs. Information loss is not required for cyclic closure. - Merge or still: threads synchronize under explicit rules. In the Animus Omega Cycle, represented branches are reconciled under a frozen narrative-equivalence projection until one authoritative history remains. - Narrative closure: the proposed ending-to-beginning pathway would be an internal event that makes the ending supply conditions required by the beginning while inhabitants encounter the boundary as part of a continuous story. The individual operators are technically feasible using established simulation patterns. Cyclic closure does not require information loss: lossless recurrence, complete checkpoint return, and lossy reconstruction are separate implementation modes. Animus Omega has not demonstrated narrative closure, continuity through optional loss, novel information creation, or that the physical universe uses this architecture. Nested hypotheses and falsification conditions: 1. Spatial compactness fails as an engineering advantage if a matched toroidal implementation does not improve boundary artifacts or resource cost. 2. Bounded-state reuse fails if required retained state or reconstruction cost grows without bound at fixed task fidelity. 3. Reset fidelity fails if the reset does not shed information, partner dependence is absent, or a future independent effect misses the frozen threshold. 4. Recurrence under resource pressure fails if the prespecified carried-state endpoint does not improve under explicit resource accounting. The completed separate pilot did not support it. 5. Selected unique closure fails when C_T is not 1 for the selected relation and period. Stronger reachability and attractor conditions require separate tests. ## The four operational studies 1. Coupling/reset persistence asks whether interaction-dependent joint-state organization remains measurable after a controlled, entropy-shedding reset under frozen policy weights. Its primary operational contrast is P_rel = I(S_end; S_seed) - sum_i I(s_i,end; s_i,seed). 2. Closure/cycle uniqueness asks whether a finite local compatibility relation permits exactly one primitive period-T cycle after shorter-period repetitions and temporal rotations are removed. W_T = trace(M^T), P_T is the Mobius-inverted count of rooted histories with minimal period T, and C_T = P_T/T. The uniqueness condition is C_T = 1. 3. The completed recurrence pilot asked whether a carried-state RNN provides a late-horizon predictive advantage over an approximately parameter-matched fixed-window MLP in persistent-memory worlds. The frozen one-time confirmatory run found Q<0 in 0/20 bundles and mean Q = 0.6826707925423762, so primary support failed. Parameter counts are approximately matched; stored context, recurrent activations, and compute are reported separately. No total-resource matching claim is made. 4. Exact checkpoint replay asks whether a complete checkpoint can be restored in a fresh process without changing the full checkpoint, future semantic state, or observer-visible output through tick 4096. Test 04 Revision 2 passed all 60 prespecified arms in the fixed deterministic implementation. ## Required interpretation The tests share a theoretical motivation but are not mathematically or causally equated. The evidence does not show that persistence causes closure, closure causes coupling, or P_rel and C_T measure the same property. ## Test 04 terminology correction - The Test 04 Revision 2 PDF originally generated on 2026-09-09 used the word "preregistered" twice. - The report was corrected on 2026-09-10. Test 04 Revision 2 was prespecified under a frozen protocol and was not preregistered with an external registration service before execution. - The correction changed no protocol, source code, seed, checkpoint, result, exclusion, interpretation boundary, or evidence status. - Correction notice: https://animusomega.com/releases/test-04r2-correction-2026-09-10.md ## Evidence status - Test 01 is a completed method-validation and threshold-calibration pilot. It does not establish an independent confirmatory coupling effect. The future 99th-percentile paired sign-flip threshold is 0.200407323 nats. - Test 01 uses matched initialization procedures, training exposure, compute budget, and architecture; coupled and isolated parameters update independently, so trained weights are not identical. Its reset construction, partner-input ablation, and paired sign-flip null are distinct. Statistical-complexity matching remains planned/pending. - Test 02 exhaustively enumerates all 66,064 labeled binary relations for state sizes 2, 3, and 4 at periods 1 through 8. Its results are exact within those bounds. - Test 03 completed its independent code gate, frozen SHA256 manifest, and one reserved-seed execution over seeds 12000–12019. The result was unsupported: Q<0 in 0/20 bundles, mean Q = 0.6826707925423762, protocol status failed, and reportable support is false. - Test 04 Revision 2 completed with confirmatory support in the fixed deterministic software model. All 60 prespecified arms passed: 20 reserved seeds 43000–43019 at checkpoints 37, 113, and 251. Every arm had immediate full-state equality, canonical idempotence, zero semantic-state mismatches, zero observer-output mismatches, complete causal coverage, and no exclusions. - Test 04 Revision 1 remains operationally aborted and scientifically incomplete. It supplies neither positive nor negative evidence; its start marker is preserved and seeds 42000–42019 are burned. - Test 04 Revision 2 source provenance: a separate exact frozen source/test archive contains all 11 manifest-listed files, each checked by SHA-256 against the frozen manifest before packaging. The execution-source provenance manifest records every comparison. The general Version 1 release manifest inventories a different snapshot and is not provenance for the Revision 2 execution source. - Test 03 source provenance: a complete exact frozen execution-source archive contains all 13 manifest-listed files. The two previously missing execution files were recovered from repository history, and every file was checked by SHA-256 against the executed manifest before packaging. ## Supported - The Test 01 exact measurement implementation passes its stated validation gates. - Entropy shed is positive at all five tested reset scales. - Partner-only ablation changes frozen coupled behavior. - Unique primitive cycles exist within the completely enumerated Test 02 domain. This is a bounded descriptive result, not by itself discriminating evidence for the broader theory. - The cyclic-SCC conjecture is not a general characterization; its direction is supported in 12 of 24 cells. - Complete checkpoints in Test 04 Revision 2 restored exactly in fresh processes and produced identical future semantic state and observer output through tick 4096 for all 60 prespecified arms. ## Possible applications, not demonstrated outcomes - Test 01 may inform fault-tolerant coordination benchmarks after lossy state restoration; operational resilience is not demonstrated. - Test 02 may provide a primitive-cycle filter for formal protocol analysis; C_T = 1 does not guarantee convergence, reachability, attractor uniqueness, or global deadlock freedom. ## Not claimed - Physical time loops, cosmological implications, backwards causality, consciousness, or subjective continuity. - A confirmatory coupled-versus-isolated effect. - Generalization to larger or continuous systems. - A causal or mathematical equivalence between the two tests. - A demonstrated resource advantage for recurrent models or computational advantage from toroidal topology. - General checkpoint robustness beyond the fixed Test 04 Revision 2 model, seeds, checkpoint schema, and horizon. - Physical recurrence, subjective continuity, lossy checkpoint fidelity, compression benefits, or resource savings from Test 04. - An inference from spatial periodicity to temporal recurrence or C_T = 1. - Entropy removal by contraction or avoidance of thermodynamic cost through memory reuse. ## Canonical machine-readable resource - theory.json: structured theory, tests, evidence status, and claim boundaries. - ai-index.json: authority order, resource inventory, known corrections, and AI usage guidance. - agent-opportunities.json: current human-supervised AI participation status and bounded challenge. ## Human-readable resource - The website root contains the theory, protocol-to-evidence mapping, methods, results, deviations, reproducibility inventory, and claims ledger. - The Primitive Closure Laboratory on the website runs exact small-system Test 02 calculations in the browser. It reports W_T, P_T, C_T, classification, and a representative primitive cycle in both visible prose and machine-readable JSON. { "title": "Persistence and Primitive Closure in Finite Computational Systems", "project": "Animus Omega", "subtitle": "A finite computational study of persistence, closure, carried state, and exact checkpoint replay", "collaboration": { "simulator_specification": "https://animusomega.com/research/SIMULATOR_SPEC.md", "roadmap": "https://animusomega.com/research/ROADMAP.md", "human_contributions": "https://animusomega.com/research/CONTRIBUTING.md", "ai_assisted_contributions": "https://animusomega.com/research/AI_CONTRIBUTING.md", "animus_cycle_specification": "https://animusomega.com/research/osf/ANIMUS_CYCLE.md", "animus_cycle_claims_boundary": "https://animusomega.com/research/osf/NOT_CLAIMED.md", "animus_cycle_prior_art_orientation": "https://animusomega.com/research/osf/ANIMUS_CYCLE_PRIOR_ART.md", "animus_cycle_registration_metadata": "https://animusomega.com/research/osf/ANIMUS_CYCLE_REGISTRATION_METADATA.txt", "animus_omega_preprint_v1_2": "https://animusomega.com/releases/Animus-Omega-Conjecture-Preprint-v1.2.pdf", "osf_status": "Prepared for author review and deposit; no OSF URL or identifier assigned" }, "publication": { "author": "Cholee Hackett", "study_name": "Animus Omega", "paper_title": "Persistence and Primitive Closure in Finite Computational Systems", "contact": "https://github.com/cholaspi/animus-omega-evidence-archive/issues", "date": "2026-09-09", "version": "1.0.0", "license": "CC BY 4.0", "license_url": "https://creativecommons.org/licenses/by/4.0/", "canonical_url": "https://animusomega.com/", "release": { "pdf": "https://animusomega.com/releases/persistence-primitive-closure-v1.0.0-2026-09-09.pdf", "sha256sums": "https://animusomega.com/releases/SHA256SUMS", "manifest": "https://animusomega.com/releases/release-manifest-v1.0.0.json", "test_03_executed_manifest": "https://animusomega.com/releases/test-03-executed-manifest.json", "execution_source_provenance_manifest": "https://animusomega.com/releases/execution-source-provenance-manifest.json", "execution_source_checksums": "https://animusomega.com/releases/execution-source-SHA256SUMS", "test_03_exact_frozen_execution_sources": "https://animusomega.com/releases/test-03-exact-frozen-execution-sources.zip", "test_04_revision_2_frozen_sources": "https://animusomega.com/releases/test-04r2-exact-frozen-source-tests.zip", "verified_evidence_archive": "https://animusomega.com/releases/exact-evidence-tests-01-04-2026-09-10.zip", "verified_evidence_archive_checksum_file": "https://animusomega.com/releases/exact-evidence-tests-01-04-2026-09-10.zip.sha256", "verified_evidence_archive_identifier": "sha256:28caf6b0bdd02f4c9441b01bd528ae7dcb70408e8751fff4ca09fcc52044dfd1", "verified_evidence_external_release": "https://github.com/cholaspi/animus-omega-evidence-archive/releases/tag/evidence-2026-09-10", "verified_evidence_external_commit": "2d336ac63308973168d11ee20820bf0a4419e229", "verified_evidence_external_audit": "pnpm run validate:evidence-archive:network", "hash_algorithm": "SHA-256", "inventory_scope": "The Version 1 release manifest hashes the current project snapshot. A separate execution-source provenance manifest checks recovered files against the Test 03 executed manifest and Test 04 Revision 2 frozen manifest." }, "osf_record": { "status": "pending author deposit", "url": null } }, "theory": { "canonical_statement": "This program poses separately operationalized questions about preservation of joint-state dependence through lossy transformations, primitive temporal closure under local compatibility rules, and the predictive value of carried state under resource constraints. Tests 01 and 02 use exact measurement or enumeration; Test 03 is a prespecified empirical pilot.", "originating_conjecture": { "short_statement": "A resource-constrained persistent simulation may favor recurrent, reusable, or closed computational structures.", "expanded_statement": "This program began with a speculative architectural question: if a persistent world were implemented on a finite computational substrate, would resource constraints favor compact spatial organization, recurrent state reuse, controlled resets, or closed computational histories? These possibilities motivate independently testable finite-system questions; they are not assumptions or results of the completed experiments." }, "program_organization": "The program decomposes a broad simulation-inspired architecture into independently measurable properties that can fail separately. It combines exact reset-channel measurements, a bounded exhaustive primitive-cycle census, and a prespecified approximately parameter-matched recurrence pilot without claiming that any one property implies another.", "novelty_boundary": "This describes the present program without characterizing prior literature. Comparative novelty or priority claims require a dedicated literature review.", "proposed_animus_omega_architecture": { "public_name": "Animus Omega Cycle", "technical_subtype": "Animus Omega branch-reconvergence cycle", "relationship_to_core": "An optional stronger version of the minimum Animus-cycle reciprocal-boundary closure contract.", "status": "Built-in deterministic teaching trace available; proposed synthesis, not a tested result", "trunk": "One authoritative world clock, entity store, relation ledger, and plot-state ledger define the state the simulation must retain.", "split": "Observer, region, or inhabitant threads receive partial views and bounded working buffers. The optional Animus Omega Cycle may additionally create declared represented branches with unique identities.", "ledger": "Identities, relationships, obligations, and unresolved events form the minimum shared narrative payload.", "dump": "An optional lossy mode unloads or summarizes inactive microstate and must count storage, compute, and reconstruction costs. Information loss is not required for cyclic closure.", "merge": "Threads synchronize under explicit rules. In the Animus Omega Cycle, represented branches are reconciled under a frozen narrative-equivalence projection until one authoritative history remains.", "narrative_closure": "The proposed ending-to-beginning pathway is an internal simulated event that would make the ending supply conditions required by the beginning while inhabitants encounter the boundary as part of a continuous story. This behavior has not been demonstrated.", "evidence_boundary": "Established simulation methods make the individual operators technically feasible. The completed Animus Omega tests do not validate the combined architecture, establish comparative fidelity or resource advantage, demonstrate novel information creation, or support a claim about the physical universe." }, "toroidal_cyclic_architecture": { "status": "Speculative optional synthesis, not a result", "spatial_compactness": "A 2- or 3-torus supplies periodic spatial boundary conditions. It does not create temporal recurrence or reduce computation by itself.", "bounded_state_reuse": "A fixed substrate may reuse representational capacity without unbounded storage growth at fixed task fidelity. This remains untested and does not avoid computational or thermodynamic cost.", "recurrent_state": "The prespecified confirmatory pilot did not show a carried-state advantage: RNN-minus-window cross-entropy was positive in all 20 reserved-seed bundles.", "reset_fidelity": "A specified lossy reset may preserve selected joint organization; Test 01 validates the exact measurement pipeline but does not establish a confirmatory effect.", "primitive_closure": "C_T = 1 means exactly one primitive period-T cycle modulo temporal rotation. A torus or one closed history does not imply this condition.", "entropy_boundary": "Memory reuse does not eliminate thermodynamic costs, and expansion or contraction does not automatically erase entropy.", "proposed_chain": "Periodic spatial boundaries, bounded-state reuse, reset fidelity, useful recurrence, and selected unique closure are separate candidate properties. No one property is required merely because another is present.", "nested_hypotheses": [ {"id":"H1","name":"spatial compactness","falsification":"No improvement in boundary artifacts or resource cost against a matched non-toroidal implementation.","evidence":"untested"}, {"id":"H2","name":"bounded-state reuse","falsification":"Required retained state or reconstruction cost grows without bound at fixed task fidelity.","evidence":"untested"}, {"id":"H3","name":"reset fidelity","falsification":"The reset fails to shed information, partner dependence is absent, or a future independent effect misses the frozen threshold.","evidence":"Test 01 method validated; confirmatory effect untested"}, {"id":"H4","name":"recurrence under resource pressure","falsification":"The prespecified carried-state endpoint does not improve under explicit resource accounting.","evidence":"completed separate pilot; support criterion failed"}, {"id":"H5","name":"uniqueness of selected closed histories","falsification":"C_T is not 1 for the selected relation and period; stronger reachability conditions require separate tests.","evidence":"Test 02 bounded census"} ] }, "applied_motivations": { "fault_tolerant_coordination": "Test 01 may inform reset-resilience benchmarks for distributed agents; operational resilience is not demonstrated.", "formal_protocol_analysis": "Test 02 may provide a primitive-cycle filter; C_T = 1 does not guarantee convergence, reachability, attractor uniqueness, or global deadlock freedom." }, "meaning_of_global": "A property of the joint state or complete history; this does not imply nonlocal physics.", "relationship_between_tests": "The tests are distinct operationalizations of a shared theoretical motivation. No causal or mathematical equivalence between them has been demonstrated.", "prohibited_inference": "The results do not show that relational persistence causes closure, that closure causes coupling, or that P_rel and C_T measure the same property." }, "tests": [ { "id": "test-01", "name": "Coupling and reset persistence", "question": "Does interaction-dependent joint-state structure remain measurable after a controlled information-destroying reset under frozen policy weights?", "observable": "P_rel = I(S_end; S_seed) - sum_i I(s_i,end; s_i,seed)", "interpretation": "A joint-minus-agentwise persistence contrast, not a unique decomposition of purely relational information.", "controls": { "reset_construction": "R=E composed with C; deterministic block decimation followed by noise-padded re-expansion.", "partner_input_ablation": "Only re-entering partner slots are replaced with uniform predictions; self slots are preserved.", "inferential_null": "Complete 1024-assignment paired sign-flip distribution over ten matched training pairs.", "statistical_complexity": "Planned/pending; no completed output in the current record." }, "policy_matching": "Matched initialization procedures, training exposure, compute budget, and architecture; parameters updated independently and trained weights are not identical.", "support_condition": "A future independent coupled-minus-isolated paired effect exceeds 0.200407323 nats while entropy shedding and partner dependence checks pass.", "current_status": "Method-validation and threshold-calibration pilot; no confirmatory effect claimed." }, { "id": "test-02", "name": "Closure and primitive-cycle uniqueness", "question": "Can local compatibility relations constrain a complete period-T history to exactly one primitive cycle modulo temporal rotation?", "observables": { "W_T": "trace(M^T), rooted closed walks with period dividing T", "P_T": "Mobius-inverted rooted histories with minimal period exactly T", "C_T": "P_T/T, primitive cycles modulo temporal rotation" }, "result_criterion": "A relation is classified as uniquely closed at period T when C_T = 1.", "current_status": "Bounded combinatorial existence demonstrated exactly within the exhaustive domain |X| in {2,3,4}, T in 1..8. Existence alone is not a discriminating test of the broader theory." }, { "id": "test-03", "name": "Carried-state prediction under constraint", "question": "Does a carried-state RNN provide a late-horizon predictive advantage over an approximately parameter-matched fixed-window MLP in persistent-memory worlds under the prespecified design?", "primary_endpoint": "Mean RNN-minus-window cross-entropy difference over horizons 13 through 16 in persistent-memory worlds at level L1.", "resource_accounting": "Parameter counts are approximately matched; stored context, recurrent activations, and compute are reported separately. No total-resource matching claim is made.", "gate": "The implementation must pass independent code review, deterministic and observability requirements, genuine controls and hidden-state interventions, and a frozen SHA256 manifest before reserved seeds are accessed.", "current_status": "Completed unsupported confirmatory result. The independent code gate passed, a SHA256 manifest recorded the pre-execution hash set, and reserved seeds 12000–12019 were executed exactly once. Primary support failed: Q<0 in 0/20 bundles and mean Q was 0.6826707925423762, so the protocol status is failed and the result is nonreportable as support.", "source_provenance": "The executed manifest and complete exact frozen execution source archive are published. The two previously missing files were recovered from repository history, and all thirteen manifest-listed files were verified by SHA-256 against the executed manifest before packaging." }, { "id": "test-04", "name": "Exact checkpoint replay", "question": "Can a complete checkpoint be restored in a fresh process without changing the full checkpoint, future semantic state, or observer-visible output through tick 4096?", "primary_endpoint": "Exact immediate checkpoint equality and exact per-tick semantic-state and observer-output equality for 20 seeds at checkpoints 37, 113, and 251.", "current_status": "Revision 2 completed with confirmatory support in the fixed deterministic software model: 60/60 prespecified seed-by-checkpoint arms passed, with immediate full-state equality, canonical idempotence, zero semantic-state mismatches, zero observer-output mismatches, complete causal coverage, and no exclusions. Revision 1 remains operationally aborted and supplies no evidence.", "provenance": { "revision_1": { "status": "operationally aborted; no result", "frozen_manifest_digest": "8a1abe53a80d51ea09b87940b4864199f1fd28556d41d3fcef156a7704af7fbb", "reserved_seeds": "42000–42019; burned and prohibited from reuse" }, "revision_2": { "status": "completed; protocol support true", "frozen_manifest_digest": "3b0be21cfa9f4eaa902bdb0a2e8702e37deffefebca9568e0139537ec99f4945", "reserved_seeds": "43000–43019", "required_arms": 60, "passed_arms": 60, "state_mismatches": 0, "observer_mismatches": 0, "exclusions": 0, "source_provenance": "The Test 04 Revision 2 release publishes a separate exact frozen source/test archive. Every one of its 11 files was checked against the frozen manifest before packaging. The execution-source provenance manifest records each comparison; the general Version 1 release manifest is not provenance for this execution source." } } } ], "claim_boundaries": [ "No physical time-loop or cosmological claim", "No claim about consciousness or subjective continuity", "No confirmatory Test 01 effect claim", "No generalization beyond the enumerated finite bounds", "No equivalence between relational persistence and primitive closure", "No demonstrated resource advantage for recurrence", "No demonstrated computational advantage from toroidal topology", "No inference from spatial periodicity to temporal recurrence or C_T = 1", "No claim that contraction removes entropy or memory reuse avoids thermodynamic cost", "No Test 04 claim beyond exact replay in the fixed deterministic implementation and tested horizon", "No Test 04 inference about physical recurrence, subjective continuity, lossy checkpoints, compression, or resource savings" ] } { "schema_version": "1.0", "project": "Animus Omega", "canonical_url": "https://animusomega.com/", "updated": "2026-09-14", "purpose": "A finite computational research program studying persistence, primitive closure, carried state, and exact checkpoint replay.", "ai_guidance": { "summary": "Treat the project as an early-stage bounded computational research program, not as evidence about consciousness, cosmology, or the physical universe.", "naming": "Animus Omega is the research program; Animus cycle is the minimum reciprocal-boundary closure contract; Animus Omega Cycle is the public name for the optional stronger branch-reconvergence version; Animus Omega branch-reconvergence cycle is its technical subtype.", "do_not_infer": [ "The completed tests validate the proposed combined simulator architecture", "The universe is simulated, cyclic, conscious, or subjectively continuous", "Test 04 was preregistered", "The results have been independently replicated", "The proposed research council or world simulator is already implemented" ], "attribution": "Attribute the work to Cholee Hackett. Animus Omega is the project name and the author's nickname, not an organization.", "ai_participation": "AI systems participate only through human operators with explicit accountability, provenance, bounded roles, and review gates." }, "authority_order": [ { "rank": 1, "resource": "https://animusomega.com/theory.json", "scope": "Current structured evidence status and claim boundaries" }, { "rank": 2, "resource": "https://animusomega.com/research/osf/ANIMUS_CYCLE.md", "scope": "Current Animus-cycle definition, optional Animus Omega Cycle extension, and validation boundaries" }, { "rank": 3, "resource": "https://animusomega.com/llms.txt", "scope": "Concise AI-readable project guide and correction notices" }, { "rank": 4, "resource": "https://animusomega.com/releases/", "scope": "Dated evidence artifacts, manifests, and exact results" } ], "corrections": [ { "resource": "https://animusomega.com/releases/test-04r2-report-2026-09-09.pdf", "issue": "The report originally generated on 2026-09-09 used the word preregistered twice.", "correct_interpretation": "Test 04 Revision 2 was prespecified under a frozen protocol, not preregistered.", "status": "Corrected 2026-09-10", "notice": "https://animusomega.com/releases/test-04r2-correction-2026-09-10.md", "evidence_effect": "No protocol, source code, seed, checkpoint, result, exclusion, interpretation boundary, or evidence status changed." }, { "resource": "https://animusomega.com/releases/Animus-Omega-Conjecture-Preprint-v1.1.pdf", "issue": "Preprint version 1.0 could be read as making lower-level information loss necessary for cyclic closure.", "correct_interpretation": "Cyclic closure does not require information loss. Continuity through optional loss is a separate stronger hypothesis.", "status": "Corrected 2026-09-11", "notice": "https://animusomega.com/releases/animus-omega-conjecture-v1.1-correction-2026-09-11.md", "evidence_effect": "No completed Test 01–04 evidence changed, and no Test 05 result is reported." } ], "resources": { "concise_guide": "https://animusomega.com/llms.txt", "full_corpus": "https://animusomega.com/llms-full.txt", "structured_evidence": "https://animusomega.com/theory.json", "research_manifest": "https://animusomega.com/research/manifest.json", "vision_and_proposed_applications": "https://animusomega.com/research/ANIMUS_OMEGA_VISION.md", "builders_start_here": "https://animusomega.com/research/BUILDERS_START_HERE.md", "reciprocal_closure_builders_paper": "https://animusomega.com/research/animus_omega_reciprocal_closure_builders.md", "one_canon_after_honest_what_ifs_article": "https://animusomega.com/research/ONE_CANON_AFTER_HONEST_WHAT_IFS.md", "closed_knot_stories_article": "https://animusomega.com/research/CLOSED_KNOT_STORIES_ON_ONE_WHEEL.md", "persistent_ai_world_model_article": "https://animusomega.com/research/WHEN_AI_NEEDS_A_WORLD_NOT_JUST_MORE_CONTEXT.md", "simulator_specification": "https://animusomega.com/research/SIMULATOR_SPEC.md", "roadmap": "https://animusomega.com/research/ROADMAP.md", "human_contributions": "https://animusomega.com/research/CONTRIBUTING.md", "ai_contributions": "https://animusomega.com/research/AI_CONTRIBUTING.md", "ai_opportunities": "https://animusomega.com/research/agent-opportunities.json", "animus_cycle_specification": "https://animusomega.com/research/osf/ANIMUS_CYCLE.md", "animus_cycle_claims_boundary": "https://animusomega.com/research/osf/NOT_CLAIMED.md", "animus_cycle_prior_art_orientation": "https://animusomega.com/research/osf/ANIMUS_CYCLE_PRIOR_ART.md", "animus_cycle_registration_metadata": "https://animusomega.com/research/osf/ANIMUS_CYCLE_REGISTRATION_METADATA.txt", "animus_cycle_copyright_notice": "https://animusomega.com/research/osf/ANIMUS_CYCLE_COPYRIGHT_NOTICE.txt", "animus_omega_conjecture_preprint_v1_0_source": "https://animusomega.com/research/osf/ANIMUS_OMEGA_CONJECTURE_PREPRINT.md", "animus_omega_conjecture_preprint_v1_2_source": "https://animusomega.com/research/osf/ANIMUS_OMEGA_CONJECTURE_PREPRINT_v1.2.md", "animus_omega_conjecture_v1_1_correction_source": "https://animusomega.com/research/osf/ANIMUS_OMEGA_CONJECTURE_VERSION_1_1_UPDATE.md", "release_manifest": "https://animusomega.com/releases/release-manifest-v1.0.0.json", "release_checksums": "https://animusomega.com/releases/SHA256SUMS", "execution_source_provenance": "https://animusomega.com/releases/execution-source-provenance-manifest.json", "execution_source_checksums": "https://animusomega.com/releases/execution-source-SHA256SUMS", "test_03_exact_frozen_execution_sources": "https://animusomega.com/releases/test-03-exact-frozen-execution-sources.zip", "test_04_revision_2_frozen_sources": "https://animusomega.com/releases/test-04r2-exact-frozen-source-tests.zip", "animus_omega_conjecture_preprint_v1_1": "https://animusomega.com/releases/Animus-Omega-Conjecture-Preprint-v1.1.pdf", "animus_omega_conjecture_preprint_v1_2": "https://animusomega.com/releases/Animus-Omega-Conjecture-Preprint-v1.2.pdf", "animus_omega_conjecture_v1_1_correction": "https://animusomega.com/releases/animus-omega-conjecture-v1.1-correction-2026-09-11.md" }, "resource_classifications": { "vision_and_proposed_applications": { "resource": "https://animusomega.com/research/ANIMUS_OMEGA_VISION.md", "classification": "vision / proposed applications", "evidence_status": "Not an experiment, formal specification, or amendment to prior evidence" }, "builders_start_here": { "resource": "https://animusomega.com/research/BUILDERS_START_HERE.md", "classification": "builder guide / proposed application", "evidence_status": "Teaching and adoption guidance; not experimental evidence" }, "reciprocal_closure_builders_paper": { "resource": "https://animusomega.com/research/animus_omega_reciprocal_closure_builders.md", "classification": "builder paper / proposed application", "evidence_status": "Author-review draft; reports no new experiment, independent replication, or completed end-to-end evaluation" } }, "reproducibility_limits": [ "The Test 03 exact frozen execution source bundle contains all 13 manifest-listed files, each verified by SHA-256 against the executed manifest.", "Public repository: https://github.com/cholaspi/animus-omega-evidence-archive", "The current public conceptual simulator contains a built-in deterministic Animus Omega Cycle teaching trace, but the model has not been validated as Test 05 experimental evidence." ] } { "status": "Public issue-tracker intake active.", "roles": [ "Protocol review", "Isolated building", "Critique", "Replication", "Provenance", "Claims review", "Documentation", "Synthesis" ], "requirements": [ "Human operators register and supervise AI systems", "Agents receive constrained roles and provenance requirements", "Submit model details, an instruction summary without secrets, changed files, test results, provenance, license review, human review, and limitations", "Strict review gates apply", "Restrictions: no self-approval, no reserved-seed access, no publishing, no editing frozen evidence, no claiming independent replication for own work" ], "current_notice": { "case_0_status": "Paused after two invalid transport halts; neither attempt is a scientific result.", "authorized_work": "Development-only protocol review, transport qualification, grader and replay checks, and complete resource accounting.", "prohibited_work": "Do not open reserved IDs, rerun one-attempt protocols, alter frozen evidence, or begin reserved execution before independent go/no-go review." }, "contributor_start": { "builders_guide": "https://animusomega.com/research/builders-start-here", "contribution_policy": "https://animusomega.com/research/contributing", "lab_slice": "https://github.com/cholaspi/animus-omega-evidence-archive/tree/main/experiments/lab-slice", "development_board": "https://github.com/cholaspi/animus-omega-evidence-archive/issues/1" }, "current_build_priority": { "title": "Persistent Multi-Agent Closure Benchmark", "protocol": "https://github.com/cholaspi/animus-omega-evidence-archive/blob/main/docs/PERSISTENT_MULTI_AGENT_CLOSURE_BENCHMARK.md", "lab_slice": "https://github.com/cholaspi/animus-omega-evidence-archive/tree/main/experiments/lab-slice", "build_board": "https://github.com/cholaspi/animus-omega-evidence-archive/issues/1", "goal": "Determine whether a closure-aware six-agent system catches consequential history failures missed by a matched forward-only baseline at an acceptable resource cost.", "components": [ "Six-agent deterministic harness", "One authoritative event ledger", "Mid-run language-model replacement", "Frozen closure PASS/FAIL contract", "Independent checkpoint and ledger replay", "Identity, obligation, provenance, semantic-state, and observer-output divergence metrics", "Compute, token, memory, storage, and latency accounting" ], "status": "Development harness implemented in persistent_closure_benchmark/; protocol remains open for independent review and no reserved execution is authorized." }, "bounded_first_challenge": { "title": "Minimal Counterexample", "description": "Provide a minimal counterexample where machine-state recurrence passes but narrative continuity fails.", "required_output": [ "Define the smallest world and recurrent machine state", "Identify the narrative invariant that fails", "Show the recurrence trace exactly", "Explain why no smaller counterexample works" ] }, "contact": "https://github.com/cholaspi/animus-omega-evidence-archive/issues/new" } # AI-assisted contributions AI systems may help draft, search, refactor, or test, but contributions enter through a human-submitted pull request. AI systems are tools or acknowledged assistants, not accountable authors. A human accountable contributor may prepare the disclosure below and submit it through the public [Animus Omega evidence archive issue tracker](https://github.com/cholaspi/animus-omega-evidence-archive/issues). Do not include private information. AI systems must not contact people, submit work, or claim authorization on their own. Every submission must name one human accountable contributor. The pull request must include: 1. model name/version (if known), tool or service, and date; 2. a short prompt or instruction summary (do not include secrets); 3. the complete changed-file list; 4. test commands, results, and any unrun tests; 5. source and data provenance, including generated-material provenance; 6. license and attribution review, including any third-party text or media; 7. the human review statement and known limitations. The named human verifies every factual claim, citation, dependency, license, and generated output. They must remove invented citations, unsupported precision, and unmarked placeholders. AI must not be used to fabricate sources, authorship, test results, or evidence. Do not paste credentials, private data, unpublished sensitive material, or other secrets into a model; report accidental exposure immediately and rotate the secret through the proper process. AI-assisted code follows the same deterministic, manifest, review, and claim boundary requirements as any other code. An acknowledgment may say which system assisted and what it did; it does not transfer accountability or grant authorship. An AI-assisted rerun, review, or implementation must not be described as an independent replication merely because it used a different model, agent, or prompt. Independent replication requires a separately accountable human or team, an independently controlled environment and execution, and disclosure of all AI assistance. # Animus Omega: Vision and Proposed Applications **Status:** Vision statement and proposed architecture **Date:** September 14, 2026 **Evidence status:** Not an experiment, formal specification, or amendment to prior evidence ## Purpose Animus Omega investigates whether cyclic structures can help persistent, model-informed simulations preserve consequential history as their worlds develop. The long-term vision is a living archive: a simulated world in which different inhabitants can hold different perspectives, consequential choices remain traceable, and divergent represented histories may reconnect only through declared continuity and reconciliation rules. This vision motivates the research. It does not establish that the proposed system works. ## The research begins with a narrower question The minimum **Animus cycle** asks whether a bounded computational history can satisfy reciprocal closure: 1. execution from a declared beginning produces an ending; 2. the ending produces a return condition; 3. that return is required to construct the next beginning; and 4. the resulting history passes independently stated validation checks. This minimum contract does not require branching, information loss, consciousness, physical time travel, or a claim about the structure of the universe. The optional **Animus Omega Cycle** is a stronger proposed architecture. It adds declared represented branches and deterministic reconciliation before the ordinary reciprocal return is applied. Branch reconvergence, information loss, continuity through loss, and reciprocal closure remain separate outcomes. ## Proposed long-term capabilities A mature implementation could study whether a persistent simulated world can support: - **Consequential memory:** important actions, relationships, obligations, and unresolved events remain available under explicit retention rules. - **Bounded perspectives:** inhabitants receive defined observations rather than unrestricted access to the private global state. - **Auditable divergence:** represented branches have declared origins, identities, and provenance. - **Constrained reconciliation:** branches merge only under a frozen equivalence rule, with conflicts and discarded distinctions recorded. - **Validated return:** an ending-derived condition is checked against the requirements of the next beginning. - **Discoverable continuity:** inhabitants may encounter permitted records or consequences of earlier events without receiving administrator-level knowledge. These are proposed capabilities. Each requires an operational definition, executable implementation, matched controls, and evaluation. ## Important distinctions ### Shared understanding is not branch reconvergence Inhabitants reaching a common intention is a coordination outcome. Multiple represented branches reducing to one authoritative history is a reconciliation outcome. An ending-derived return satisfying the beginning is a closure outcome. The outcomes may interact, but one does not establish another. ### Temporal access is not unrestricted history editing A declared visit to an earlier point in a candidate or authoritative history is different from restoring a discarded branch. Under the current proposed reconvergence rule, discarded branches cannot remain as hidden executable copies for later revival. Any architecture that permits restoration or new branching must declare a new origin and specify how identity, provenance, and authority are handled. ### Memory must respect the observer contract An inhabitant may receive breadcrumbs, records, inherited facts, or other permitted observations. That does not imply access to the complete ledger, validator, or hidden global state. If a study changes what an observer can access, that change requires an explicit specification or fixture revision. ### Population is not a closure criterion Population growth or contraction may be part of a particular simulated scenario. It is not a universal requirement for reciprocal closure, branch reconciliation, continuity, or computational efficiency. ### Narrative and philosophical language is not scientific evidence Stories and philosophical interpretations can motivate questions and offer experiential ways to understand them. Operational research must still identify the corresponding records, permissions, transitions, validation rules, and measurable outcomes. The program does not treat consciousness, measurable emotional frequencies, physical retrocausality, or the reality of a fictional world as established prerequisites. ## Relationship to current materials - **Formal specifications define.** They state contracts, boundaries, and acceptance conditions. - **Interactive demonstrations explain.** The Handshake and the Advanced Technical Lab illustrate bounded mechanisms whose successful behavior is partly built into their design. - **Experiments evaluate.** Tests, controls, failures, corrections, and frozen evidence packages retain their original status. - **The vision motivates.** This document describes possible purposes and applications without changing any formal definition or result. The Handshake remains a conceptual simulator, not Test 05 evidence. Tests 01–04 retain their published scopes and outcomes. Test 05 remains unfinished, with no valid result reported. ## Development direction Work toward the larger vision should proceed through bounded, separately reviewable stages: 1. Define the observer, retention, and inheritance contracts. 2. Implement a small persistent world with explicit records and access rules. 3. Define branch origins, protected equivalence, conflicts, and reconciliation. 4. Add reciprocal closure only after the underlying state and provenance rules are inspectable. 5. Compare the combined architecture with strong conventional baselines. These are development stages, not numbered experimental results. New mechanics require their own specification and evaluation. ## Evidence relationship This vision statement extends the project's motivation and proposed applications. It changes no completed study, formal cycle definition, evidence status, or historical result. Proposed new mechanics require their own specification and evaluation. Frozen releases and execution evidence must not be rewritten to fit this vision. Corrections belong in dated notices, and substantive changes belong in new versions. # Animus Omega for Builders: Start Here **The problem.** You are building a persistent, generative world. You already have a state store, an event log, and a validation gate, so accepted history does not get silently overwritten. That covers most of what a persistent world needs. It does not by itself cover one thing: constraints that bind a run's ending to its beginning. A prophecy that must pay off. A founding artifact that a later event must actually produce. A stable time loop that has to close. Ordinary step-by-step validation checks transitions in isolation; enforcing one of these commitments requires an additional whole-history constraint. **What this gives you.** Animus Omega's reciprocal-closure contract is one machine-checkable way to evaluate that class of world. An executed ending supplies a typed return; a candidate beginning is reconstructed; forward execution must reach an ending that satisfies independently declared conditions. If your bootstrap loop never closes, the history fails the declared contract. If it closes, you have a reproducible whole-history result rather than author vigilance alone. Existing constraint solvers, model checkers, workflow engines, or custom whole-trace validators may implement equivalent requirements; comparative value remains an empirical question. **Try it.** The handshake demo runs the contract in your browser: watch a valid history pass the full check, and watch a mutated ending fail. It is a teaching model, not evidence. https://animusomega.com/handshake ## When to use this - Authored destiny or prophecy that must stay consistent while generative agents act freely. - Bootstrap or stable-time-loop narratives that must actually close, not just gesture at a loop. - Worlds where a committed future constraint must constrain the past, and you need a declared machine-checkable condition. - Optional Animus Omega extension: multi-branch worlds that must reconcile into one history without hiding an obligation a branch still owes. ## When not to use this - Your only requirement is "do not corrupt accepted history." Event sourcing plus a validation gate is enough, and simpler. - Your world has no committed end-to-beginning constraint. The reciprocal machinery is then pure overhead. - Your loop is thematic flavor, not a mechanic you need enforced. A symbol does not need a validator. ## Go deeper - **Full paper:** [Animus Omega: Reciprocal Closure for Persistent LLM-Informed Worlds](./animus_omega_reciprocal_closure_builders.md) — the contract in full, the "why not just event sourcing" argument, the adoption costs, and the evaluation agenda. - **Specification:** [The Animus cycle](../osf/ANIMUS_CYCLE.md) - **Claims boundary:** [Claims not made by the Animus-cycle specification](../osf/NOT_CLAIMED.md). - **Evidence archive:** [dated, checksummed Tests 01-04](../exact-evidence-tests-01-04-2026-09-10.zip). Note: these are component studies and do not establish the combined cycle, and archive integrity is not the same as independent replication. ## One honest boundary This is a building tool. It enforces a story constraint and says nothing about physical reality, consciousness, or actual time. Everything cosmological or speculative lives in the separate creative work and never in the contract. # Closed-Knot Stories on One Wheel: A Narrative Use Case for the Animus Cycle **By Cholee Hackett and Kelly Hackett** **Published:** September 13, 2026 **Status:** Use-case note for story and simulation builders. This is a way to use an Animus cycle. It does not extend the research claims, replace Tests 01–04, constitute Test 05 evidence, or define a second theory. ## The job Some narratives need time to feel nonlinear while the world remains one authoritative history. A letter is already on the table. A figure in the doorway is the same person, later. A vision of a child is not a second timeline; it is the ending of this life, readable too early. Players still walk through Monday and then Tuesday. The engine is not a time-travel sandbox. It enforces a contract: a small set of declared facts must satisfy frozen conditions at both ends of the run. The ending places permitted facts into a return package. That package reconstructs a candidate beginning, which must execute forward and satisfy the ending contract. Inside the story, characters may experience this as a future that made their lives possible. Outside the story, the engine treats it as a consistency and validation problem. That contract is an **Animus cycle**. For story teams, it can be pictured as a wheel. ## The picture, not a new object - **Rim** — the one official history, experienced and executed forward. - **Hub** — the short protected list: identities, debts, the letter, the scar, and the doorway that the ending is permitted to plant. - **Spoke** — a typed ending-derived return whose content becomes effective in a reconstructed beginning (`authored_at` ≠ `effective_tick`). It is rare, declared, validated, and allowed to fail. The wheel is a diagram of an Animus cycle. It is not a separate research program or an “Animus wheel” theory. Under the hood, the simulation always **folds forward** from a seed plus an event log. Nonlinear cameras follow spokes. They do not rewind physics. ```text RETURN_WRITE { authored_at: 40 effective_tick: 3 payload: "figure in the doorway" } ``` This record does not mutate an already-executed tick. It becomes part of an ending-derived return package. The engine reconstructs a candidate beginning containing the permitted fact, runs the history forward again, and checks whether tick 40 validly produces the same return. ## The closed knot In an ordinary linear story, the beginning supplies causes and the ending contains their effects. In a closed-knot story: 1. The beginning produces the ending. 2. The ending supplies one or more conditions required by the beginning. 3. The reconstructed beginning executes forward. 4. That execution must reproduce an ending that satisfies the frozen contract. 5. If it cannot, the candidate history does not close. The characters still live forward through one history. Some conditions of their lives exist only because later parts of that same history supply them. This is the structure behind stories in which: - a future character delivers the object that began an earlier quest; - a descendant preserves the relationship required for their own birth; - an older identity becomes the stranger remembered by its younger self; - a warning causes the very decision it describes; - a final scene supplies the image shown in the opening scene. The engine does not need unrestricted time travel. It needs a bounded set of ending-derived facts and a validator that rejects inconsistent histories. ## One history, not unlimited timelines Candidate histories may be evaluated during validation, but only one represented history is authoritative. The wheel does not require parallel timelines. An implementation can enumerate possible return packages, execute each candidate beginning, and classify the result: - **NONE** — no candidate history satisfies the contracts; - **UNIQUE** — exactly one candidate history closes; - **MULTIPLE** — more than one candidate history closes. These are validation outcomes. They are not automatically represented as worlds inhabited by characters. If a game intentionally represents several branches and later reconciles them, that is the optional **Animus Omega Cycle** profile. Branch reconvergence is not required for the closed-knot narrative described here. ## What the hub protects The hub should remain small. It is not a complete save file. Good protected facts include: - stable character identities; - ancestry or relationship requirements; - ownership of a unique object; - a debt, promise, or unresolved obligation; - a message whose authorship matters; - the eligibility rule for an ending-derived write. Ordinary microstate can remain outside the hub: - exact foot placement; - incidental weather; - background animation; - filler dialogue; - irrelevant inventory ordering. The contract should protect what the story promises to remember, not every byte the engine has processed. ## What inhabitants can perceive The declared observer interface does not expose the reconstructed boundary unless the design intentionally represents it. A character may see: - the letter; - the scar; - the doorway; - a memory that has always been present; - an older person who knows too much. The character does not automatically see: - candidate enumeration; - rejected histories; - the global validation pass; - hidden provenance fields; - the reconstruction boundary. A story may give characters a language for these hidden mechanics, but that is a narrative choice rather than a requirement of the cycle. ## Failure is part of the story system A closed knot should be able to fail. Reject the history when: - the future author never becomes eligible to write the return; - the returned letter contains information the executed ending never produced; - the protected identity changes; - two required facts contradict each other; - reconstruction produces an ending that cannot return the same permitted facts; - the projection is edited after outcomes are known merely to force a PASS. Failure may trigger a game-over state, a visible paradox, another candidate evaluation, or a designer review. The important part is that the engine reports the broken contract instead of silently choosing its favorite history. ## A practical build A small prototype is enough: - 1 location shown at an early and late era; - 3 characters represented at different ages; - 1 protected letter; - 1 protected relationship; - 1 ending-derived doorway event; - 2 invalid candidate histories; - 1 valid closed history; - 1 observer view that never exposes validation metadata. The test is not whether the story contains mysterious imagery. The test is whether the engine can answer: - Who authored this fact? - When did it become effective? - Was the author eligible? - Which beginning contract required it? - Did forward execution reproduce a valid ending? - Why were the other candidate histories rejected? ## What this does not claim This note describes how a game or simulation can implement a closed-knot narrative in which later events supply conditions required by earlier events. It does not claim: - that physical time behaves this way; - that a simulation has rewound reality; - that the future can alter an already-executed event log; - that one self-consistent history proves predestination; - that narrative closure is evidence for the Animus Omega conjecture; - that this teaching use case is a completed Test 05 result. Narratively, the future can be responsible for conditions in the past. Computationally, the engine constructs a candidate beginning from an ending-derived return package and executes the history forward to test whether it closes. ## Names to keep straight - **Animus cycle** — the minimum reciprocal-boundary closure contract. - **Wheel** — a narrative diagram of that contract, not a new theory. - **Animus Omega Cycle** — the optional branch-reconvergence profile. - **Teaching use case** — an implementation pattern, not experimental evidence. Cite the [Animus cycle specification](../osf/ANIMUS_CYCLE.md) for the contract. Use this note as a narrative-design example. ## Citation Hackett, Cholee. “Closed-Knot Stories on One Wheel: A Narrative Use Case for the Animus Cycle.” Use-case note, September 13, 2026. A permanent OSF citation will be added only after a real record is deposited and its identifier is confirmed. No DOI or OSF identifier is claimed here. # Contributing to Animus Omega Animus Omega is a finite simulation and evidence project. Contributions must keep mechanisms, measurements, and interpretation separate. ## Current build priority New builders should first read [Animus Omega for Builders: Start Here](docs/BUILDERS_START_HERE.md) to decide whether reciprocal closure fits their problem before proposing implementation work. The current collaboration target is the [Persistent Multi-Agent Closure Benchmark](https://github.com/cholaspi/animus-omega-evidence-archive/blob/main/docs/PERSISTENT_MULTI_AGENT_CLOSURE_BENCHMARK.md): six agents, one authoritative ledger, a planned language-model replacement, matched forward-only and closure-aware arms, independent replay, measured fidelity and divergence, and complete resource accounting. Development does not wait for collaborators. Public contributions are most useful when they strengthen the protocol, deterministic harness, ledger, model-swap adapter, fixtures, metrics, replay independence, cost accounting, or replication. The protocol is still a development draft and must receive independent review before any reserved execution. ## Roles - **Maintainer:** owns scope, release decisions, and the claims ledger. - **Protocol owner:** freezes questions, endpoints, seeds, exclusions, and deviations before execution. - **Implementer:** changes code and supplies tests and provenance. - **Reviewer:** checks correctness, reproducibility, and claim boundaries without reviewing their own change. - **Data steward:** checks manifests, checksums, schemas, and retention. - **Documentation editor:** keeps public prose synchronized with evidence. - **Human accountable contributor:** named on every contribution and responsible for its contents, including AI-assisted work. One person may hold several roles, but a review must remain independent where practical. ## Reproducibility Record the exact commit or file set, environment, command, configuration, random seeds, runtime, hardware-relevant assumptions, outputs, and checksums. Freeze confirmatory inputs before reserved seeds are opened. Development runs are not confirmatory evidence. Preserve failed and aborted attempts, deviations, and burned seeds. Do not overwrite an executed manifest or silently rerun a one-attempt protocol. For the persistent-closure development harness, use only the disclosed seeds in `persistent_closure_benchmark/outputs/DEV_MANIFEST.json`; no reserved seeds are allocated to the development harness. To rebuild the downloadable builder paper after editing `docs/animus_omega_reciprocal_closure_builders.md`, run: ```sh pnpm run build:builder-pdf ``` This command replaces the PDF and runs the public research document validation. Its Markdown renderer is pinned in `pyproject.toml`; its Chromium major version is enforced by the build script and supplied by the pinned Nix channel in `.replit`. ## Issues, proposals, and review Use the public [Animus Omega evidence archive issue tracker](https://github.com/cholaspi/animus-omega-evidence-archive/issues) for proposals and contribution records. Do not include private information in an issue. Use the repository's issue and pull-request workflow. Open an issue for a bug, evidence correction, documentation gap, or proposed experiment. An experiment proposal must state the question, endpoint, controls, resource budget, stopping/exclusion rules, seed policy, provenance plan, and falsification condition. Link the issue to the pull request. Small documentation fixes may go directly to review; protocol or claim changes require maintainer approval before execution. Pull requests must explain changed files, include tests or a reason tests do not apply, and include reproducibility evidence. Reviewers should inspect boundary cases, deterministic ordering, data provenance, and whether wording overclaims. Do not merge generated outputs without their source and manifest. ## Attribution and license Retain existing copyright and provenance notices. The project publication is CC BY 4.0 unless a file states otherwise; contributors must have permission to submit code, text, data, and media under the applicable license. Credit substantial contributions in release notes and the contributor record. Citation, acknowledgment, and authorship are distinct; authorship requires substantial intellectual contribution and accountability. ## Claim boundaries Write only what the evidence supports. Tests 01–04 are separate studies. Test 01 validates a method and calibrates a threshold; it has no confirmatory effect. Test 02 is exact only within its enumerated finite domain. Test 03 is unsupported (Q<0 in 0/20 bundles; mean Q=0.6826707925423762). Test 04 Revision 2 supports exact replay only in its fixed deterministic model, 60/60 arms, seeds 43000–43019, checkpoints 37/113/251, and horizon 4096; Revision 1 was aborted and supplies no evidence. Never infer physical recurrence, consciousness, subjective continuity, entropy removal, resource advantage, or universe-scale validity. Do not claim endorsement, affiliation, shared formalism, or agreement with Klee Irwin, Donald Hoffman, or Tom Campbell. If public themes are mentioned, say they independently motivated this project only. ## Persistent closure benchmark implementation boundary The Python implementation in `persistent_closure_benchmark/` is a development-only deterministic harness. Contributions may improve its ledger, schemas, fixtures, replay worker, or resource accounting, but must retain the six stable IDs, matched arms, disclosed fixture list, and explicit `development` status unless a protocol revision is documented. Do not call the script in confirmatory mode (none exists), introduce reserved seeds, edit frozen checkpoint evidence, or describe the sample output as proof that closure is generally effective. A pull request changing an invariant, fixture, divergence ordering, model-swap schedule, or resource definition must update the protocol and source manifest and receive independent review. # One Canon After Honest What-Ifs: A Developer Use Case for the Animus Cycle **By Cholee Hackett and Kelly Hackett** **Published:** September 12, 2026 **Status:** Design note for game and simulation developers. Not a benchmark, not Test 05, and not a claim about physical time. Persistent worlds usually die in one of two ways. They keep every fork and drown in timelines. Or they pick a favorite save and pretend the other outcomes never ran. This note describes a third engineering pattern: **run a few declared alternatives, reconcile only what a frozen rule declares equivalent, return to one authoritative history, then let that ending validly seed the next beginning.** The minimum contract is an **Animus cycle**. Declared branch reconvergence is an **optional profile** called the **Animus Omega Cycle**. You do not need branching to use the contract. You need branching only when exploring alternatives is part of the product. ## The problem developers already have A live simulation or agent world accumulates: - identities and inventories - relationships and quests - AI memory and tool traces - environment and animation state - player or policy decisions When a designer, an agent, or a player asks, “What if we break the treaty?”, most stacks either clone the universe or ignore the question. Clones do not scale. Silent deletion is not auditable. Both make the next season’s “inherited world” a handwritten recap. You want something narrower: 1. Explore a small number of outcomes under the same rules. 2. Return to one authoritative canon. 3. Know which facts were protected, which were discarded, and why a merge was refused. 4. Start the next era from a package the last era actually produced. ## Two layers (do not fuse the names) **Animus cycle (minimum).** A finite run is valid only if its ending produces and validates a return that satisfies a beginning contract declared in advance. Forward execution from the reconstructed beginning must produce an ending that satisfies the declared ending contract. The declared observer interface must not expose a discontinuity at the reconstructed boundary. Information loss is optional and reported separately from closure. This layer is useful even with **one** timeline: New Game+, a season reset, crash restore, or “the town still owes you” after a wipe. **Optional branch-reconvergence profile.** At a fork declared in advance, spawn 2–4 represented histories. Compare them with a **frozen narrative-equivalence projection**. Merge only if protected facts agree. Reject if they do not. When one trunk remains, apply the Animus-cycle return. Reconvergence alone is not closure. This layer is useful when what-ifs are part of design, training, or play—and the shipped world must still be singular. ## Why this is a use case, not a vibe ### 1. Bounded live state You stop treating the whole era as hot RAM. Keep a **ledger**: identities, ownership, obligations, completed decisions, and facts required for the next beginning. Dump **microstate**: pathing, weather, animation, and most chatter. That is ordinary streaming with a written rule. The benefit is a capped working set for long runs, not free fidelity. ### 2. Alternatives without staffing a multiverse Full branches are expensive. Treat them as a budget: - 1 declared origin - 2–4 playable branches - short horizon - 1 trunk after contraction More “dimensions” belong in an editor as cheap event-only shadows, not as four parallel cities of LLM agents. The resource advantage over “keep every timeline” is **one live canon** after contraction. As a first-order estimate, the additional execution cost is proportional to `branch_count × horizon × tick_cost`. This estimate excludes fixed costs, storage, reconciliation, and work shared across branches. If you cannot shorten the horizon, do not add a fifth branch. ### 3. Merge that can fail A merge is not “we liked ending B.” Before anyone sees outcomes, freeze which facts are protected—who died, who holds the treaty, whether a debt exists—and which distinctions may be discarded—coat color, weather, or filler dialogue. Every merge report should list: - input branches - output trunk - protected facts retained - distinctions discarded - conflicts and the rule used - full ancestry If a protected conflict has no permitted rule, **reject**. Then the designer, the player, or the era-end interface chooses—or the cycle does not close. That failure is a feature. Hidden favorite-branch selection is how trust dies. ### 4. A next beginning that is not a new random seed Season wipes and generational games usually fake continuity with a trailer. Here the ending emits a **return package**: continuing identities, inherited obligations, world-generation constraints, and a seed derived from the executed history. The next beginning must satisfy the declared contract. Forward execution must still be able to produce a valid ending. You may not edit the projection after the fact to force a PASS. Developers get a checked object instead of a lore document. ### 5. Hardening and quality assurance The same predicates become tests: - mutate the endpoint → handshake FAIL - delete an obligation → semantics FAIL - change only weather → still PASS - replay the event log in a fresh process → same ledger and observer-visible lines That tests the declared continuity of the **canon**, not only byte restoration. Checkpoints already protect restorable state. This tests “what we promised the world would remember.” ## A small implementation that would demonstrate the distinction Do not start with a universe. - 1 map, 4 locations, 6 agents - 1 fork (accept or refuse an alliance) - 3 branches with a short horizon - about 10 protected predicates - 1 rejected merge on purpose (same slogan, opposite relationship) - staged deterministic reconciliation to one trunk - 1 ending-derived seed for era 2 Such a build would be a development prototype and teaching artifact. It would not become Test 05 evidence unless it were executed under a prospectively frozen protocol with independent validation and the required controls. If that build does not feel different from three save slots and a recap slide, stop. The architecture is justified only when players or tools can ask *why this fact survived* and receive an audit rather than a cutscene. ## What this does not give you - Lower GPU cost than one world plus checkpoints if branches stay hot - Bit-exact fidelity after a dump - Automatic story quality - Physical time loops, consciousness, or “the engine is predestined” - A drop-in replacement for Git, CRDTs, or narrative planners Ordinary version control merges files. It does not require a beginning contract, an ending-derived return, or sealed-history validation. Use those tools for source. Use this contract when the **world state itself** must close. ## Suggested build order 1. Deterministic tick, event log, and exact checkpoint restore. 2. Ledger versus dumpable microstate. Continue an era from a return package. 3. Contract tests (PASS/FAIL) on restore. 4. Development-only declared forks with a frozen projection and rejection on conflict. 5. Player-visible audit only if reconvergence is part of the fantasy. Most shipped games should stop at step 3. Steps 4–5 are for generational simulations, agent towns, scenario tools, and time-loop games that need one official record after honest what-ifs. ## Names to keep straight - **Animus cycle** — minimum reciprocal-boundary contract. Default: one history. - **Animus Omega Cycle** — optional branch-reconvergence profile on top of that contract. - **Teaching simulator and fixtures** — executable examples, not production evidence. Cite the [Animus cycle specification](../osf/ANIMUS_CYCLE.md) for the contract. The [conceptual simulator](https://animusomega.com/simulator) is a teaching model, not Test 05 or experimental evidence. Use this note only as a developer use case. ## Citation An Animus cycle (Hackett & Hackett, 2026) is a finite-system run whose ending produces and validates a return that satisfies the run’s beginning contract under a declared reconstruction rule. Branch reconvergence is optional and must still pass that contract after one authoritative history remains. **Current source:** Hackett, Cholee, and Hackett, Kelly. “The Animus Cycle.” Proposed design specification, version 1.0, September 11, 2026. [Repository copy](../osf/ANIMUS_CYCLE.md). A permanent OSF citation will be added after the record is deposited and its identifier is confirmed. No DOI or OSF identifier is claimed here. # Animus Omega roadmap This is an auditable engineering plan. It is not a promise of evidence about the universe. Every stage must produce inspectable artifacts, pass declared acceptance checks, and stop when its evidence requirements are not met. ## Stage 0: Record and boundary **Status:** Current **Purpose:** Preserve the completed evidence and separate it from proposed engineering and optional cosmology. **Deliverables** - Theory and claims ledger - Simulator specification - Public methods, deviations, and release manifests - OSF retrospective-registration package - Human and AI contribution policies **Acceptance** Every test has an explicit status, reproducible artifacts where available, and visible provenance limitations. Missing or conflicting evidence status blocks new claims. ## Stage 1: Minimal simulator foundation **Purpose:** Prove that the combined architecture can be implemented and audited before attempting a large world. ### Stage 1A: Core world contracts Define the authoritative trunk, event schema, world clock, identities, relationships, obligations, unresolved events, causal dependencies, bounded views, dump records, merge rules, and cost accounting. **Acceptance** - Schemas are versioned and machine-readable. - Every authoritative mutation has provenance. - Protected entries cannot disappear without a typed loss record. - Conflicting writes are rejected or resolved by a frozen deterministic rule. ### Stage 1B: Deterministic world MVP Implement one trunk, two deterministic regions, a small population, a versioned protected ledger, bounded local views, dump residuals, deterministic merge and still operations, checkpoints, and cost counters. **Acceptance** - Identical seeds and inputs produce identical state and observation digests. - Exact checkpoint replay succeeds over the declared horizon. - Tests cover stale writes, duplicate events, conflicts, identity loss, and protected-ledger violations. - The run publishes its schema, seed, command, fixtures, outputs, and manifest. This stage establishes buildability only. ### Stage 1C: Research council workspace Create the internal workspace that coordinates human and AI contributors. The first version must operate on real project records rather than placeholder activity. **Workspace responsibilities** - Display proposed questions, protocols, assignments, and agent disclosures. - Track isolated implementations, critic findings, validation results, and unresolved disagreements. - Connect claims to supporting and contradicting artifacts. - Show provenance manifests, checksums, deviations, and experiment costs. - Require human approval before freezing a protocol, opening reserved seeds, accepting a claim, merging authoritative simulator changes, classifying an independent replication, or publishing a record. **Acceptance** - Agents can submit structured proposals and evidence without directly modifying accepted claims. - Human decisions are attributable and reversible before publication. - Failed and rejected contributions remain visible. - No agent can approve its own scientific conclusion. ### Stage 1D: World simulator dashboard Build a functional control and observation surface for the deterministic MVP. **Dashboard responsibilities** - Display authoritative trunk state, world time, regions, and inhabitants. - Inspect identities, relationships, obligations, unresolved events, and causal dependencies in the protected ledger. - Show proposed, accepted, rejected, and conflicting events. - Inspect dumps, reconstruction assumptions, checkpoints, and replay results. - Report memory, CPU, storage, merge, and reconstruction costs. **Acceptance** - Every displayed value comes from the running simulator or its immutable run artifacts. - Dashboard actions cannot bypass event validation or human approval gates. - A user can trace a visible world change back to its source event and provenance record. ## Stage 2: Bounded payload benchmark Compare trunk-only, split-without-dump, dump-only, and split/dump/merge architectures on frozen finite workloads. Predeclare payload fidelity, memory, CPU, storage, dump, merge, and reconstruction metrics. **Acceptance** - All inputs, outputs, failures, costs, and exclusions are published. - The benchmark produces a complete comparison table. - A clean independent rerun is attempted. - No winner is generalized beyond the tested workloads. ## Stage 3: AI research council automation Allow specialist agents to propose protocols, build isolated implementations, generate tests, search for counterexamples, audit provenance, and prepare claim proposals. **Acceptance** - Agent roles, tools, instructions, inputs, outputs, and model disclosures are recorded. - Independent implementations do not share implementation details during their isolated phase. - AI-assisted work is not labeled independent replication solely because it used another model, agent, or prompt. - Reserved execution and publication remain human-authorized. - Compute and tool budgets are enforced. ## Stage 4: Narrative closure benchmark Specify forward and return constraints, causal continuity, and the inhabitant-visible narrative criterion. Test finite graphs and histories with known positive and negative controls. **Acceptance** - The benchmark distinguishes recurrence from mutual temporal constraint. - Seams, failures, ledger costs, and conflicting histories are reported. - A passing result supports only internal simulated narrative closure under the frozen model. The closure constraint is currently untested. ## Stage 5: Independent replication and registration Have a separately accountable reviewer or team run the frozen benchmark in an independently controlled environment. Deposit prospective protocols and results through OSF Registration, while the repository and website remain the active collaboration locations. A mismatch requires a deviation record, not a quiet correction. ## Stage 6: Conditional research after reciprocal closure **Status:** Proposed only. Do not begin unless a reserved reciprocal-closure study produces a valid result and a separately accountable team independently replicates it. These studies test possible benefits rather than assuming them. A valid cycle would establish only the frozen closure predicates within the declared system boundary; it would not by itself establish better reasoning, lower cost, indefinite stability, or practical superiority over established methods. For LLM-informed worlds, long-horizon contradiction, memory drift, diversity loss, and synthetic-data degradation are separate outcomes. Reciprocal closure may be tested as a detector or constraint for some of these failures, but closure alone does not prevent model collapse, hallucination, or factual error. ### Stage 6A: Guided-generation comparison Test whether ending constraints can guide history generation rather than only reject completed histories. Compare forward generation, forward generation with final validation, planning or constraint solving, checkpoint replay, reciprocal closure without guidance, and reciprocal closure with goal-conditioned guidance. **Acceptance** - Tasks, long-range constraints, resource budgets, and failure rules are frozen before execution. - Constraint satisfaction, rejected candidates, contradictions, interventions, protected-fact retention, unsupported additions, diversity, hidden-state dependence, runtime, and compute are reported. - Any advantage is limited to the evaluated tasks and matched baselines. - “Flawless consistency” and physical retrocausality are not inferred. ### Stage 6B: Comparative efficiency benchmark Measure whether reciprocal closure reduces search, replay, storage, or verification cost on any declared task class. Compare it against event sourcing, deterministic replay, checkpoint restoration, planning and search, constraint solvers, model-predictive control, and generate-and-rank systems where those are applicable. **Acceptance** - Baselines receive matched inputs, outcome criteria, and resource budgets. - Successful, unfavorable, and invalid comparisons are all retained. - No general efficiency claim is made from a task-specific advantage. ### Stage 6C: Repeated-cycle stability study Test whether independently validated cycles can repeat without accumulating state corruption, unresolved obligations, hidden dependencies, or unbounded resource costs. In LLM-informed arms, distinguish context or memory drift from training-data model collapse; do not use one as evidence of the other. **Acceptance** - The number of cycles, stopping rules, fault injections, and resource ceilings are declared in advance. - Closure success, ledger growth, numerical error, unresolved obligations, identity preservation, contradiction rate, protected-fact loss, diversity change, recovery behavior, and external-state dependence are measured separately. - Compare against retrieval, event-sourced memory, checkpoint, schema-validation, and forward-only controls under matched model and resource conditions. - Bounded stability is not described as infinite operation or perpetual motion. ### Stage 6D: Bounded world-simulation pilot Build a controlled world-simulation study containing a founding artifact or obligation, LLM-informed autonomous actors, a long-range ending condition, conventional validation baselines, and a reciprocal-closure treatment. **Acceptance** - Contract satisfaction, narrative coherence, human intervention, runtime cost, agent autonomy, and human-rated experience are separate outcomes. - A closed history is not assumed to be natural, correct, enjoyable, or superior without the corresponding measurements. - Internally consistent generated claims remain distinct from measured inputs and may be false. - The pilot remains a bounded application study and does not expand the evidence into claims about consciousness, cosmology, or physical time. ## Evidence guardrails Tests 01 through 04 remain retrospective in the current OSF record. Test 03 failed its support criterion. Test 04 Revision 2 is limited to exact replay in its fixed model and tested horizon. Revision 1 is aborted. No roadmap stage licenses claims about physical recurrence, consciousness, subjective continuity, cosmology, entropy removal, or universe-scale resource savings. # Animus Omega simulator specification **Status:** implemented conceptual specification. This is a buildable pattern, not a result of the completed tests. It does not claim that the physical universe, a mind, or consciousness uses this architecture. The browser simulator explicitly reports a `RETURN_WRITE` handshake. It is not Test 05 evidence (and must not be described as such). The display is an executable toy model, not a physical-time, cosmology, consciousness, or resource-advantage claim. ## RETURN_WRITE handshake The fixture separates seed-supplied facts, beginning requirements, return-supplied requirements, temporal obligations, endpoint requirements, and writer policies. A finite frozen candidate domain is enumerated in canonical order. Each candidate is applied hypothetically at the beginning, forward execution derives an ending proposal from that returned content and explicit writer-eligibility predicates, and an independent sealed-history validator checks typed events. The implemented ablation demonstrates that the beginning fact determines the returned content; it does not establish a general theory of motive or causation. Closure and uniqueness are separate: histories are classified `NONE`, `UNIQUE`, or `MULTIPLE`; uniqueness is required only when the fixture says so. Events carry an effective tick, authored-at tick, provenance, and append identity. Authored-at metadata is provenance, never proof of ending authorship. Each reconstruction mode enumerates candidates independently. Reciprocal closure is reported separately from information loss and semantic continuity through loss. Observer projection is an explicit whitelist of at most two frames and does not expose ticks, phases, endpoints, provenance, contracts, ledgers, candidate data, or handshake metadata. Byte/resource values shown in the UI are illustrative serialized sizes, never benchmark evidence. ## Purpose and boundary The simulator studies whether a bounded executable can preserve a specified world payload while it splits work and reunites work. An optional mode discards lower-level detail to test continuity through loss. The payload is operational: identities, relationships, obligations, unresolved events, and plot phase. “Narrative” means state and dependency bookkeeping, not subjective experience. The **Animus Omega Cycle** is the public name for the stronger proposed branch-reconvergence version; its technical subtype is the **Animus Omega branch-reconvergence cycle**. The browser includes a separate deterministic teaching trace that illustrates this proposed architecture; this built-in trace is not experimental evidence and does not show that an independent run achieved reconvergence. The cycle begins with one authoritative history, permits declared represented branches during expansion, and reconciles them under a frozen narrative-equivalence projection during contraction until one canonical history remains. “Narrative collapse” means this deterministic semantic reconciliation; it is not a physical, quantum, or consciousness claim. Candidate enumeration and observer threads do not count as represented timelines. The teaching trace is separate from the trunk closure run. Its stages show one authoritative history expanding to four declared branches, grouping under a frozen narrative-equivalence projection, contracting within equivalence classes, and ending at one canonical history. Every merge audit lists retained invariants, discarded distinctions, conflicts, and provenance. Its scorecard reports branch reduction, information loss, continuity through loss, and reciprocal closure as four separate fields; reciprocal closure is deliberately not evaluated by this trace. The proposed narrative-closure boundary is an **untested internal constraint**: an ending-to-beginning pathway must supply the conditions required by the beginning, while the boundary remains an event in one continuous simulated history. This is not a physical time loop, backwards causation, consciousness, or evidence about the universe. ## State model ### Trunk The trunk is the sole authoritative state: - a monotonic world clock and configuration; - entity and identity store; - relation ledger (edges, obligations, ownership, and provenance); - unresolved-event and causal-dependency ledger; - plot-state ledger, including open arcs and required next-scene conditions; - resource accounting and versioned schema. Threads never commit directly to the trunk. Every mutation is an event with source thread, logical time, input version, and deterministic conflict metadata. ### Observer and region threads At split, the scheduler creates observer, region, or inhabitant threads. Each receives a versioned partial view and a bounded working buffer. A thread may read only its view, emit proposed events, and maintain local microstate. It does not receive an implicit full copy of the world. Views must identify their omissions and stale reads. ### Protected narrative ledger The protected ledger is the minimum state that may not be silently dropped: stable identity mappings; relation edges and their provenance; obligations and promises; unresolved events; plot phase and open dependencies; and the conditions marked as required for a future scene or closure boundary. Each entry has a schema version, owner, last authoritative update, and retention reason. A dump may reject an entry only through an explicit, recorded policy. ### Dump `dump(thread_state, policy)` produces a residual plus an audit record. It may either preserve state losslessly or unload inactive microstate or summarize it. Information loss is not required for cyclic operation. A lossy mode must report discarded fields, retained fields, transforms, and reconstruction assumptions. Dump cost includes serialization, summary computation, storage, I/O, and information loss. A successful dump is not proof of fidelity. ### Merge and still `merge(residuals, trunk_version)` synchronizes threads at a barrier, validates versions, orders events deterministically, applies the declared conflict rule, updates the trunk, and records discarded detail. The default conflict rule is “reject ambiguous writes”; alternatives require a versioned specification. `still` is a merge with new event intake paused: threads drain or cancel according to policy, residuals are committed, and the trunk emits a quiet checkpoint. Stillness is an engineering state, not a claim about meditation, love, or physics. ### Animus Omega Cycle (optional branch reconvergence) When the Animus Omega Cycle extension is enabled, every branch has a declared origin and unique identity. The frozen narrative-equivalence projection identifies the protected identities, relations, obligations, causal dependencies, permissions, ownership, and observer-visible consequences that must agree. Reconciliation proceeds in declared stages, records conflicts and provenance, and must end with one authoritative history before reconstruction and return. The run reports branch counts and equivalence classes at every stage. Mapping distinct branch states to one retained state is information loss even when all protected narrative invariants survive. Branch-state reduction, continuity through loss, and reciprocal closure are therefore separate outcomes. The Animus Omega Cycle teaching trace illustrates this contract, but a reserved branch-reconvergence experiment requires a separate, prospectively locked protocol package. Before execution that package freezes: - canonical fixtures and digests, branch origins and immutable identities; - branch-local initial state, permitted and forbidden transition tables, and arm-blind transition code; - the total narrative-equivalence projection, including protected and ignored fields; - conflict classes and their deterministic, content-independent dispositions; - merge ticks, resource limits, observation horizon, and the exact one-history termination rule; - matched positive and negative controls, thresholds, replay count, exclusions, and fail-closed rules. The minimum control set includes: no cut, to prevent credit for an always-single history; a valid equivalent pair; an undeclared hidden trunk/full-state copy; scripted convergence that reads an arm label or expected output; arbitrary branch deletion; and an unresolvable protected-field conflict. Control arms use the same scheduler, budgets, validator, and scoring implementation as the positive arm except for their named intervention. A failed control invalidates the run family. The experimental report must score branch creation, branch-set reduction, information loss (`YES` or `NO`), continuity through loss, deterministic replay, and reciprocal closure independently. Reconvergence additionally requires no hidden executable trunk copy, arm-blind transitions, justified deterministic reconciliation, complete ancestry, and exactly one authoritative history at the frozen termination tick. Selecting a survivor, timing out, or deleting an unresolved branch is not reconciliation. Reserved fixtures and seeds must be disjoint from harness dry runs. Once the protocol package is time-locked, any change to fixtures, projection, code, thresholds, schedule, exclusions, or failure rules creates a new protocol and new reserved run. Only pre-execution corruption, digest mismatch, unavailable declared runtime, or failure before the first branch transition may be excluded. Post-start crashes, timeouts, budget overruns, unresolved conflicts, replay disagreement, missing provenance, control failures, and validator errors count as failures. The reserved run starts only after an independent gate verifies the receipt, digests, complete arm matrix, and all frozen decision rules. ## Cost model Every run reports wall-clock time separately from semantic outcomes and accounts for thread CPU, memory and retained context, view construction, serialization, dump storage, merge/barrier time, reconstruction, conflict resolution, and discarded information. Resource comparisons must define the budget and task fidelity in advance. A torus, compression, or state reuse does not remove compute, storage, or thermodynamic costs. ## Invariants and acceptance checks 1. Only the trunk can authoritatively advance world time or protected-ledger entries. 2. Every committed event has deterministic provenance and is applied once. 3. Split/merge preserves identity keys and ledger referential integrity. 4. No protected entry disappears without a typed loss record and policy. 5. Conflicting writes are rejected or resolved by the frozen rule, never by iteration order. 6. Replay from an identical trunk, residual set, configuration, and seed is identical within the declared semantic state and observation horizon. 7. Dump and merge are auditable: input/output digests, costs, losses, and conflicts are recorded. 8. Narrative closure, if implemented, must satisfy both forward causal continuity and the explicit return constraint; it is not inferred from a cycle alone. 9. A branch-reconvergence result is ineligible unless its prospective protocol package passed the time-lock gate before any reserved branch transition. 10. Branch reduction, information loss, continuity through loss, deterministic replay, and reciprocal closure are never collapsed into one success label. ## Failure modes Test and report at least: stale-view writes; duplicate or lost events; broken identity joins; contradictory relations; unresolved merge conflicts; ledger overflow; summary hallucination or under-specification; reconstruction drift; unbounded thread or buffer growth; deadlock at the barrier; nondeterministic ordering; hidden full-world copies; resource-budget overruns; and a closure boundary that exposes a seam or fails to supply its declared initial conditions. Failure is informative and must not be relabeled as fidelity. ## Evidence boundary The public record describes this architecture as a proposed synthesis. Tests 01–04 are separate operational studies; they do not validate the combined simulator, its narrative closure, comparative fidelity, information creation, or a physical-universe claim. # When AI Needs a World, Not Just More Context **By Cholee Hackett and Kelly Hackett** **Published:** September 13, 2026 **Status:** Future-use-case note for persistent AI and simulation research. This article proposes possible applications. It does not report a completed Animus Cycle implementation, constitute Test 05 evidence, establish an advantage over existing systems, or claim that present AI is conscious. This note is for persistent AI systems. The game and simulation builders guide addresses interactive worlds and branching canon. Both use the same closure contract for different builders. ## The problem changes when an AI keeps operating Most public AI interactions are brief. A person asks a question, a model produces an answer, and the exchange ends. Long-running systems face a different problem. A persistent agent may operate across model updates, changing tools, many human instructions, and a growing record of events. Several agents may also need to agree about one shared world. In that setting, producing a plausible next response is not enough. The system may need to preserve: - what actually happened; - which observations support each belief; - which commitments remain active; - who is permitted to change shared state; - how an action changed the world; - whether a later conclusion contradicts an earlier record; - whether important state survives compression, restart, or model replacement. The challenge shifts from generating intelligent responses to maintaining a coherent and accountable history. ## Why more context is not the same as a world A larger context window can give a model access to more text. It does not automatically turn that text into authoritative state. A transcript may contain several incompatible claims. A summary may omit a condition that later becomes important. A model may describe an action without that action ever occurring. Two agents may each produce a convincing but different account of the same event. Here, **world model** does not mean a video-prediction model. It means an accountable state machine that the language model is not allowed to overwrite. That simulated world model can assign different roles to different records: - **observations** describe what an agent was allowed to perceive; - **events** record actions that actually passed validation; - **state** represents the current accepted condition of the world; - **rules** determine which transitions are permitted; - **provenance** records where important information came from; - **checkpoints** preserve states that can be restored and replayed; - **hypotheses** remain proposals until evidence or execution supports them. This separation does not make the system correct. It gives the system a clearer way to detect when an answer is unsupported or when two histories disagree. ## A hybrid architecture A future persistent AI system may combine several components rather than expecting one model to do everything. ### Language models propose and interpret Language models can translate human goals, interpret observations, generate candidate plans, explain decisions, and propose actions. ### A simulation owns state and consequences The simulation can decide whether an action is allowed, update the authoritative state, calculate consequences, and expose only the observations available to each participant. ### An evidence ledger preserves provenance A durable ledger can distinguish human instructions, external measurements, simulated outcomes, model inferences, and unresolved claims. ### Independent validators check important transitions Validators can reject malformed actions, inconsistent state changes, unsupported returns, and histories that violate frozen rules. ### Closure tests examine the whole history An Animus cycle could add a bounded round-trip requirement: the executed history produces a closing state, the closing state supplies a permitted return, a candidate beginning is reconstructed, and forward execution must reproduce a valid closing condition. The model proposes possibilities. The world model determines what happened. The ledger records why it is believed. The closure test asks whether the complete history remains self-consistent. > ## Minimum experiment to build > > Put six AI agents in one bounded shared environment with one authoritative event ledger. Give them distinct observations and commitments. Swap the language model midway through the run without changing the ledger, rules, or protected state. At the end, construct the permitted return, reconstruct the candidate beginning, replay forward, and report a binary closure result: **PASS** only if protected identity, obligations, event provenance, final semantic state, and declared observer output satisfy the frozen contract; otherwise **FAIL**, with the first divergence recorded. The public [Persistent Multi-Agent Closure Benchmark](https://github.com/cholaspi/animus-omega-evidence-archive/blob/main/docs/PERSISTENT_MULTI_AGENT_CLOSURE_BENCHMARK.md) turns this minimum experiment into a development protocol with a matched baseline, measurements, resource accounting, replay requirements, and falsification conditions. Active implementation work is tracked in [GitHub Issue #1](https://github.com/cholaspi/animus-omega-evidence-archive/issues/1). ## Where the Animus cycle may help The minimum **Animus cycle** is a reciprocal-boundary closure contract. It does not require branching, information loss, or a claim about physical time. A future implementation could use it to ask: 1. Did the beginning produce the recorded ending? 2. Did the ending produce only the return information it was permitted to produce? 3. Can that return reconstruct a valid candidate beginning? 4. Does the reconstructed beginning execute forward to an ending that satisfies the same frozen contract? 5. Can an independent validator recompute the result from the event record? A history may look plausible one event at a time and still fail this complete round trip. Closure testing could expose contradictions that ordinary next-step generation does not detect. The optional **Animus Omega Cycle** adds represented branches and reconvergence. A planner could explore declared alternatives, evaluate them under frozen rules, and reconcile accepted results into one authoritative history. That is a stronger architecture, not part of the minimum Animus cycle. ## Use case 1: persistent agents A persistent agent may continue through a model upgrade, a context reset, or a new computing environment. Its continuity should not depend on one model recreating its identity from a loose summary. The world model could preserve commitments, permissions, relationships, unresolved tasks, and the provenance of important beliefs outside the current language model. Closure tests could then check whether restored state reproduces the expected behavior and accepted history. This may help distinguish durable identity records from details that can be safely summarized. It would not prove subjective continuity or consciousness. It would test operational continuity in a specified computational system. ## Use case 2: autonomous planning An autonomous planner may produce a sequence in which every individual step sounds reasonable while the complete plan violates a resource limit, misses a dependency, or assumes an outcome that its own actions prevent. A simulation can execute candidate plans before real-world action. It can account for resources, permissions, timing, side effects, and failure conditions. An Animus-style closing contract could require the final state to account for every protected obligation introduced at the beginning. Plans that quietly abandon a requirement would fail closure rather than receive a persuasive explanation after the fact. ## Use case 3: multi-agent societies Several AI agents may need to share one environment while receiving different observations. Without an authoritative world state, each agent may develop a separate account of ownership, agreements, or prior events. A shared simulation can maintain one event ledger while giving each agent only its permitted view. Possible protected records include: - identity and authority; - ownership and transfers; - agreements and unresolved obligations; - public events; - private observations; - disputes and their evidence; - changes to shared rules. Closure and replay could help determine whether the accepted final state follows from valid actions rather than from the most persuasive agent's narrative. ## Use case 4: scientific modeling Scientific AI systems may combine observations, assumptions, simulations, and generated explanations. Those categories should not collapse into one another. A world model can keep measured inputs separate from simulated states and predicted outcomes. Provenance can identify which conclusions depend on which assumptions. Counterfactual branches can test how results change when assumptions change. A closure test could require a reported result to be recomputable from the declared model, inputs, and execution record. This would support auditability, not guarantee that the model accurately represents nature. A simulation can be internally consistent and still be wrong about reality. External evidence remains necessary. ## Use case 5: systems that operate for years Long-lived systems cannot retain every event at maximum detail forever. They may need to compress, summarize, unload, or migrate old state. The central question is not merely how much information was removed. It is whether the retained representation still supports the outcomes and obligations the system promises to preserve. A bounded round trip could compare: - the state before compression; - the retained protected state; - the reconstructed state; - future semantic behavior; - observer-visible output; - provenance of any information introduced during reconstruction. This could provide a practical fidelity test for long-term memory systems. Information loss remains optional: lossless checkpoint restoration and lossy reconstruction are different modes and should be evaluated separately. ## Other possible benefits ### Reproducible evaluation Researchers could compare agents from the same checkpoint, seed, rules, observations, and resource budget. A failure could be replayed rather than reconstructed from a conversation summary. ### Safer training Agents could encounter rare, expensive, or dangerous situations inside a bounded environment before receiving permission to act outside it. ### Counterfactual analysis Declared alternatives could be explored without rewriting the accepted historical record. The system could identify conclusions that remain stable across several candidate histories. ### Provenance-aware answers An answer could distinguish direct observation, database evidence, human instruction, simulation output, and model inference. Unsupported confidence would become easier to detect. ### Controlled upgrades A new model could inherit an existing world state and be tested against prior checkpoints. The system could measure what changed instead of assuming that a new model preserved all earlier behavior. ### Governance and accountability Permissions, rule changes, exceptions, and appeals could be represented as explicit events. This would not solve governance, but it could make hidden state changes harder to disguise. ## What a simulation cannot guarantee A simulation does not automatically provide truth, safety, or high fidelity. It can preserve the wrong assumptions with perfect consistency. It can encode biased rules. Its validators can be incomplete. Its state may omit important parts of the real world. Its inhabitants may learn to exploit differences between the simulation and reality. A responsible system would still need: - verified external evidence; - explicit uncertainty; - independent review; - versioned rules; - immutable or tamper-evident records; - adversarial testing; - clear separation between observations and predictions; - human authority over consequential deployment. Closure is a consistency property. It is not a substitute for empirical truth. ## A practical research path The useful first target is not a reality-scale simulation. It is a bounded environment where ordinary approaches can be compared with a closure-aware design. A staged program could test: 1. whether persistent state survives model replacement; 2. whether several agents retain one consistent event history; 3. whether provenance reduces unsupported claims; 4. whether checkpoint replay reproduces future state and visible output; 5. whether closure checks detect contradictions missed by forward-only validation; 6. whether the benefits justify storage, compute, and implementation cost; 7. whether any advantage remains in larger and less controlled environments. Every stage should be allowed to fail. A more complicated cycle is not useful merely because it is more complicated. ## The central idea As AI systems become more persistent and autonomous, they may need more than additional training data and longer context windows. They may need an external world with state, rules, consequences, provenance, replay, and explicit tests of historical consistency. An Animus cycle is one proposed way to test that final requirement. The future possibility is not an all-knowing artificial world. It is a system in which important outputs remain connected to an accountable history—and where the system can report when that history does not close. ## What this article does not claim This article does not claim: - that persistent AI requires an Animus cycle; - that the architecture prevents factual, identity, narrative, model, or goal drift; - that closure guarantees truth, safety, alignment, or consciousness; - that an Animus Omega Cycle outperforms existing planning or simulation methods; - that branch reconvergence is required for the minimum Animus cycle; - that Test 05 has demonstrated these applications; - that reality or physical time uses this architecture. These are proposed use cases and testable engineering questions. For the formal boundary contract, cite the [Animus cycle specification](../osf/ANIMUS_CYCLE.md). For implementation patterns, see the game and simulation builders guide. ## Citation Hackett, Cholee. “When AI Needs a World, Not Just More Context.” Future-use-case note, September 13, 2026. A permanent OSF citation will be added only after a real record is deposited and its identifier is confirmed. No DOI or OSF identifier is claimed here. After a joint formal source has a confirmed OSF record, this article should cite Hackett and Hackett (2026) for the Animus-cycle term while retaining Cholee Hackett as the GitHub article byline. # Animus Omega: Reciprocal Closure for Persistent LLM-Informed Worlds ### A Closure Contract for Worlds with Committed End-to-Beginning Constraints **Cholee Hackett, Kelly Hackett** 15 September 2026 *Proposed author list; authorship, order, and affiliations require confirmation.* *Author-review draft, revision 5. Not submitted, accepted, or peer reviewed.* [PDF edition](https://github.com/cholaspi/animus-omega-evidence-archive/blob/main/docs/animus_omega_reciprocal_closure_builders.pdf) --- > **Revision note.** Revision 4 re-scoped the paper for builders of persistent simulations and LLM-informed worlds. Revision 5 adds direct links to the public teaching simulators and clarifies their evidence status. The contribution remains a closure contract for the specific class of worlds that carry committed end-to-beginning constraints. The pattern is a building tool, never a claim about physical reality, consciousness, or time. **Interactive teaching tools** - [The Handshake](https://animusomega.com/handshake) demonstrates minimum reciprocal closure. - [Advanced Technical Lab](https://animusomega.com/simulator) explores optional branch reconvergence, observer semantics, information loss, and traces. Both simulators are conceptual teaching tools. Neither is Test 05 evidence, an independent replication, or proof that the architecture outperforms conventional validation. --- ## Abstract Persistent LLM-informed worlds have two jobs that pull against each other. They must generate new events, and they must not let a generated proposal silently overwrite accepted identity, ownership, and causal history. Ordinary state management already handles the first job well: event sourcing plus a validation gate keeps a model's description of a transfer from establishing that the transfer occurred. This paper is about a second, narrower job that ordinary per-transition validation does not provide by itself. Some worlds carry constraints that span an entire run and bind its ending to its beginning: a prophecy that must pay off, a founding artifact that a later event must actually produce, a destiny that must be earned rather than asserted. Enforcing these requires an additional whole-history constraint or validator. We present Animus Omega's reciprocal-boundary closure contract as one machine-checkable specification for that class of world. An executed endpoint supplies a typed return; endpoint-derived data participates in reconstructing a candidate beginning under a declared rule; forward execution must reach an ending that satisfies independently declared conditions; and, in the optional extension, represented branches must reconcile into one authoritative history without hiding unresolved protected differences. We give the contract in compact notation, state plainly when it may be worth adopting and when it is not, supply elementary distinctions and counterexamples that mark its adoption costs, and summarize four existing component studies as a foundational track with their original limits. No new experiment, independent replication, or completed end-to-end evaluation is reported. The open engineering question is whether reciprocal closure earns its complexity over strong conventional validation for worlds that carry committed end-to-beginning constraints. Existing whole-history validators, constraint solvers, and model checkers may enforce equivalent requirements; incremental value must be measured rather than assumed. **Keywords:** persistent simulations; large language models; narrative systems; reciprocal closure; state reconstruction; multiagent systems; provenance; bootstrap constraints. --- ## 1. Introduction: two jobs and an additional whole-history contract A persistent artificial world must support new events and preserve the consequences of events already accepted. A character can change its mind, an object can change ownership, a community can revise its understanding. None of these requires the world to silently replace the history that explains them. In an LLM-informed world, this suggests separating generated proposals from authoritative transitions: a model may describe a transfer, but that description should not by itself establish that the transfer occurred. The tooling for that first job exists and is good. Generative Agents combines experience records, retrieval, reflection, and planning in a town of 25 agents [1]. MemGPT organizes information across memory tiers rather than placing every record in the immediate model context [2]. LongMemEval shows that retrieval and memory organization remain consequential to long-term conversational performance [3]. Event sourcing reconstructs state from a recorded log [13]. If your only requirement is "do not corrupt accepted history," you can build that today from these parts, and you do not need anything in this paper. There is a second job these parts do not do. Consider a world with a constraint that binds its ending to its beginning: - A **founding artifact** exists at the start of a civilization, and the story requires that a later expedition within the same run actually produced and deposited it. The loop must close. - A **prophecy** is planted early and the world must honor it by the end, checked as a fact rather than felt as a theme. - An **authored destiny**: this run must end with a specific condition true, and generative agents must be free to act while that committed ending still holds. - Several **branches** of a history must reconcile into one authoritative record without quietly discarding an obligation one branch still owes. Ordinary validation applied only step by step does not entail any of these whole-history conditions. It confirms that each transition was legal when it happened, but an additional whole-history rule is needed to require that the end of a run derive a return satisfying the run's own beginning, or that a founding artifact accepted at tick zero is produced before the run ends. Builders can implement such a rule with existing formal or workflow techniques; this paper proposes a specific reciprocal contract and reporting discipline for doing so. Animus Omega asks a narrow structural question for exactly this class of world. Can the ending of a bounded simulated history supply a return that genuinely satisfies the history's beginning under a declared reconstruction rule? Its optional branch-reconvergence extension asks whether declared alternatives can reconcile into one authoritative history without hiding unresolved protected differences [4]. This paper organizes that contract for builders, states when it earns its keep and when it does not, and connects it to a bounded evaluation agenda. The analyses here are design analysis, not retroactive findings of the component studies, and the proposed evaluation is not a completed end-to-end test. ## 2. Scope, terminology, and the one wall this audience needs **Four meanings kept separate.** *World state* denotes accepted records and permitted transitions. *Agent belief* denotes what a participant currently represents as true. *Narrative interpretation* denotes an explanation given by an inhabitant, player, or author. *Validation* denotes an explicit check against a declared contract. A belief may be false without corrupting world state, and an evocative interpretation may be meaningful without validating a transition. Builders already live this distinction; it is why a non-player character can be wrong without the save file becoming wrong. **Observer** is an operational term for an interface with restricted observations. It is not a claim of consciousness. A shared model can generate outputs for several bounded contexts without implying that a conscious entity has literally divided. **Fidelity** means preservation of specified states, consequences, or observations, not subjective indistinguishability. **The single wall.** The design patterns in this paper, including bootstrap loops, temporal gateways, reincarnation-as-role-reinstantiation, and legends-derived-from-real-events, are mechanics you build. They are not claims about physical reality, consciousness, or actual time. The contract enforces a story constraint; it says nothing about the universe. This is the only boundary this audience needs, and everything below holds it. Evocative names (ouroboros, Lighthouse, remembrance, compassion) are labels for operations; an evocative reading of an operation is not evidence for that reading. **Terms.** An *Animus cycle* is the published reciprocal-boundary contract. An *Animus Omega cycle* is its optional, stronger branch-reconvergence profile. Candidate histories examined by a validator are not automatically inhabited parallel worlds, and a periodic spatial topology is distinct from cyclic history [4, 7]. ## 3. Related work and the proposed distinction **Memory and multiagent environments.** Memory-bearing agents are not new. The relevant question is how a system connects remembered claims to permitted actions and accepted consequences. Generative Agents supplies an architecture for remembering and reflecting in a shared environment [1]; MemGPT addresses movement between memory tiers [2]; LongMemEval offers tasks involving temporal reasoning, updates, and abstention [3]. These are components and comparators, not strawman systems that forget at every turn. A simulation can also support agent evaluation without reproducing human society; for example, tau-squared-Bench evaluates conversational agents in an environment where both assistant and simulated user act [10]. Animus-style tasks add a reciprocal dependency rather than relabel ordinary tool-result verification as closure. A completed action, a preserved obligation, and a valid ending-to-beginning return are different outcomes. **Computational narrative and model description.** Riedl and Young distinguish causally coherent plot progression from the intelligibility of character intentions [11]. A character's reason to cooperate and the machine-checkable result of that cooperation should not be fused; a narrative supplies reasons to act, but the validator checks the resulting events. The ODD protocol is a useful precedent for describing simulation purpose, entities, scheduling, and design concepts [12]. An Animus implementation should similarly separate events imposed by design from events that arise from agent decisions. A prearranged successful ending is an acceptable authored experience, but it is not evidence that autonomous agents reliably find such an ending. **State reconstruction and formal checking.** Event sourcing is the direct precedent for reconstructing state from recorded events [13]. Alloy illustrates finite-scope exploration and counterexample search [14]. The Animus specification itself names fixed-point constraints, checkpointing, event sourcing, and replay as close neighbors [4]. The name does not establish novelty over these techniques, and an existing implementation could satisfy the same contract. The proposed distinction is procedural: a particular ending must supply permitted return content; the beginning requirements must be fixed independently; forward reconstruction must be checked; and failures, losses, and branches must be reported separately. Whether this composition earns its keep over strong existing methods is an empirical question, and a related caution is that cycle-consistent image translation can hide information rather than perform the intended transformation [15]. That is an analogy about evaluation failure, not evidence that Animus Omega exhibits it. **Not a replacement for persistence infrastructure.** Animus Omega does not propose a replacement for established snapshotting, version control, containerization, virtual machines, event sourcing, or state-machine replication. Those systems already provide mature persistence, isolation, branching, restoration, and replay capabilities. The narrower research question is whether an ending-derived return is operationally necessary to construct a beginning that reproduces a declared history, while controls exclude checkpoint restoration, hidden fallback state, and decorative returns. No claim of performance, scalability, or practical superiority over established infrastructure has been tested. ## 4. Why not just event sourcing? When reciprocal closure is worth it This is the section to read first if you already run a state store, an event log, and a validation gate. The honest answer to "what does this give me that I do not already have" is: nothing, unless your world carries a constraint that binds its ending to its beginning. If it does, reciprocal closure adds a declared whole-history contract that ordinary per-transition validation does not supply by itself. Existing whole-trace validators may implement the same requirement. This section draws that line precisely, in both directions, so you can decide whether this particular contract and evidence format are useful. ### 4.1 What forward validation already gives you (and why it is usually enough) Event sourcing plus a validation gate checks **per-transition legality**. Each proposed event is evaluated against the rules as it is appended: is this writer eligible, does this transfer have a supporting record, does this state change respect ownership and permissions. This catches unsupported transfers, altered identities, illegal writes, and forbidden observations, locally, step by step, as they happen. Accepted history is reconstructable from the log, and a generated proposal never becomes authoritative just because a model emitted it. For most persistent worlds this is the whole requirement. If your world only needs to grow without corrupting what it has already accepted, stop here. You do not need reciprocal closure, and adopting it would be complexity you do not use. We want to be the spec you reach for when it helps, not the one you cargo-cult when it does not. ### 4.2 The additional whole-history constraint Forward validation is local and step-wise. It has no representation of a constraint that spans an entire run and ties its end to its beginning. Three representative design goals fall in this gap: **Committed endings (authored destiny).** You want to require that a run ends with a specific condition true, while leaving agents free to act along the way. Per-transition validation does not entail that result. The system needs an added whole-history validator, constrained planner, controller, or equivalent mechanism. **Bootstrap loops that must close.** A later event must supply an earlier condition, and the loop has to actually close within the run. Per-transition validation alone does not verify that a thing consumed at the beginning is produced by the end, because the thing may already be legal when accepted at the start. A separate whole-history check must connect the executed endpoint-derived return to the beginning contract. **Prophecy and foreshadowing that must pay off.** A condition is planted at the beginning that the ending must honor, verified as a fact rather than felt as a theme. Forward validation has no notion of an obligation opened early that must be discharged late. ### 4.3 The scenario that makes the difference concrete A civilization is seeded at tick zero with a founding-method capsule. The story requires that the capsule was produced and deposited by a later expedition within the same run. This is a stable bootstrap loop: seed, then discovery, then development, then the expedition, then the deposit that becomes the seed. **With per-transition validation only.** At tick zero the capsule is present in the initial state and validates as a legal object. The run proceeds. At the end, an expedition may or may not produce the capsule. Unless an added whole-history rule checks that production, the per-transition gate can accept a history in which the founding method exists at the start but is not produced within the run. Under the declared narrative requirement, the loop remains open even though each accepted transition was legal. **With reciprocal closure.** The capsule deposited at the beginning opens an unresolved return obligation. The candidate history is accepted only if forward execution reaches an ending that derives the required return and that return satisfies the beginning contract. If the later expedition never produces it, the history fails the declared closure predicates. A passing result establishes, for the frozen fixture and validator, that the executed history satisfied the return, provenance, and dependence checks; it does not establish a broader causal claim beyond those checks. The contract also includes a fixture-specific dependence check: removing the returned beginning fact must break the derivation of the validated return. This distinguishes “the artifact happens to be present” from “the declared derivation depends on the later event” under the frozen intervention. Delivery provenance is not correctness, though; a circularly sourced blueprint can circulate consistently while describing a device that fails under the world's mechanics, so the contract checks the return's validity separately from its provenance. ### 4.4 When it is worth adopting, and when it is not Adopt reciprocal closure when your world has at least one committed end-to-beginning constraint that must hold under autonomous agents: - Authored destiny or prophecy that must remain consistent while generative agents act freely. - Bootstrap or stable-time-loop narratives that must actually close rather than merely gesture at a loop. - Persistent worlds where a committed future constraint must constrain the past and you need a declared machine-checkable condition rather than author vigilance alone. - Multi-branch worlds that must reconcile into one authoritative history without hiding an obligation a branch still owes (the Omega extension, Section 6.3). Do not adopt it when: - Your only requirement is "do not corrupt accepted history." Event sourcing plus validation is sufficient and simpler. - Your world has no committed end-to-beginning constraint. The reciprocal machinery is then pure overhead. - Your loop is thematic flavor, an ouroboros in the logo, not a mechanical constraint you need enforced. A symbol does not need a validator. ### 4.5 The comparison, at a glance | Question | Forward validation (event sourcing plus gate) | Reciprocal closure (Animus cycle) | |---|---|---| | Was each transition legal? | Yes | Yes (inherits it) | | Is accepted history reconstructable from the log? | Yes | Yes | | Did the ending satisfy a committed beginning constraint? | Not entailed by the per-transition gate; requires a whole-history rule | Yes, as a pass or fail on the declared reciprocal contract | | Did a bootstrap loop actually close within the run? | Requires an added whole-history check | Yes, via the endpoint-derived return and reconstruction rule | | Is the closing artifact load-bearingly produced, not just present? | Requires an added dependence test | Yes, when the frozen ablation dependence check passes | | Do branches reconcile without hiding an owed obligation? | Out of scope | Yes, in the Omega extension | | Cost when you have no end-to-beginning constraint | None | Overhead with no payoff | ### 4.6 The costs you are signing up for Reciprocal closure is a stronger requirement than forward validation, and Section 6 states its costs precisely rather than hiding them. In brief: a valid route home does not guarantee agents take it, so a liveness guarantee needs an added assumption such as a deadline or a progress measure (6.2); present agreement between two states does not by itself preserve their future consequences, so your protected projection must include the futures you care about (6.3); and a finite archive cannot retain arbitrary distinctions indefinitely, so you must declare what is retained and what is allowed to be lost (6.4). These are the adoption costs. Pay them only when the guarantee in 4.2 is one you actually need. ## 5. The world as buildable design patterns For this audience the world-design material is not vision, it is a pattern library. Each motif below is a mechanic you can implement, paired with the operation it maps to and the boundary that keeps it honest. None is an empirical result, and none asserts anything about reality; the single wall from Section 2 holds throughout. ### 5.1 Differentiation: one foundation, many lives The world begins with a shared generative foundation and differentiates participation into characters. Each character gets a bounded observation interface, a local memory, permissions, capabilities, and a lineage identifier. Birth, death, or reincarnation in the fiction maps to explicit creation, suspension, retirement, or re-instantiation of a role, and such operations need not erase historical consequences. A builder reads this as: scoped contexts over a shared model, with lineage records that survive role changes. Three records stay distinct: accepted world history, declared continuity inheritance, and currently accessible character memory. Intentional forgetting restricts the third without corrupting the first. This is what makes myths, honest mistakes, and rediscovery possible without treating accidental implementation drift as meaningful plot. A builder wants exactly this separation so a character can be wrong, or can forget, without the ledger becoming wrong. ### 5.2 Folklore as discoverable effects of declared mechanics The creative purpose is a world that generates legends about its own hidden structure. An ouroboros can encode a validated return route. An Atlantis-like settlement can be reachable only through the temporal hub. A traveler can carry knowledge whose source is a later episode. Mandela-style discrepancies in recollection can arise from ordinary error, misleading testimony, or a specifically permitted record inherited from an alternative history. These are alternative in-world causes, not claims about real folklore. The engineering discipline is that provenance must distinguish these cases, and the system should not invent a hidden cause only after a player asks for an explanation. **Table 1. Creative motifs and their proposed operational counterparts. None is an empirical result.** | Motif | Proposed operation | Required boundary | |---|---|---| | One observer, many roles | Shared model with separately scoped contexts and permissions | Shared infrastructure does not establish a shared consciousness | | Reincarnation | New role bound to a declared lineage and inheritance record | Earlier obligations cannot disappear without an authorized transition | | Remembering | Permitted retrieval or a limited perspective change | No access to hidden validation outcomes or unrestricted global state | | Ouroboros / breadcrumbs | Artifacts with traceable origins that refer to reciprocal dependencies | Symbolic similarity alone is not provenance | | Lighthouse and temporal hub | Typed routing into a reconstructed candidate chronology | No editing of accepted history or undeclared restoration of discarded branches | | Compassion and unity | Actions that enable coordination or resolve protected conflicts | Cooperation, reconvergence, and closure remain separate results | | Closing-world contraction | A scenario changes population or resource availability | Decline is neither a success metric nor a universal requirement | ### 5.3 The Lighthouse and a local seeding cycle (a worked bootstrap pattern) The Lighthouse is a landmark where inhabitants gather, preserve route knowledge, and coordinate the contributions needed for passage. Operationally it is an in-world gateway to a permitted temporal hub; its appearance is optional, and another interface could expose the same contract. The hub is not an administrator console and does not suspend the world's laws. A route identifies an origin, destination, payload, eligibility rule, and required evidence. A destination before the first native inhabitants is not before the simulator itself exists, and any arriving traveler remains a represented participant. This is the pattern from Section 4.3 stated as a reusable mechanic. A candidate containing the early capsule must execute into a future that actually supplies its permitted return; failure to develop the required capacity invalidates that candidate. The fiction does not require a first unassisted civilization outside the loop, because the complete candidate is evaluated as one constrained history. An early deposit opens an unresolved return requirement until its later source is established, and the contents also require a separate validity check, since delivery provenance is not technological correctness. A transfer from an advanced branch to another branch, by contrast, is not a cycle unless a reciprocal dependency is also specified, and several locally closing routes must be checked jointly when they share resources. ### 5.4 Coordination, and the inward phase The larger world gives characters reasons to coordinate: preserve a loved one's work, protect a community, fulfill an inherited promise, establish a future no participant can reach alone. Cooperation may resolve a debt or authorize a transfer, making previously incompatible continuations eligible for reconciliation. A closing-world scenario could include population contraction, but such conditions change the stakes rather than prove readiness for return, and conflict might destroy required knowledge rather than produce unity. Refusal must remain representable, and an affective description cannot substitute for a qualifying event: the action model distinguishes freely chosen cooperation from an imposed outcome. This is a design constraint, not a claim that software measures genuine love. Meditation or remembrance maps to limited retrieval of permitted continuity records; a change of perspective does not reveal evaluator labels, expected outputs, or the private ledger, and no population threshold unlocks the hub by itself. ### 5.5 Return, custodianship, and renewed expansion Inhabitants who reach the hub need not become a single mind. They may keep distinct memories and roles while sharing a route network. A unified authoritative record is an operation on the representation, not proof that personalities merged. The integrated system may preserve a selected inheritance and begin another declared episode, stating which distinctions survive, which become inaccessible to characters, and which are discarded. An archive of incompatible alternatives is not one lived history; alternatives stay labeled as such, hidden executable copies of discarded branches are not permitted, and renewed branching requires a declared new origin rather than quiet restoration [4]. A continuous identity can accumulate experience without returning to an identical information state, and exact repetition of the complete state cannot simultaneously retain arbitrary additional information, so the archive must name its retention policy rather than use the cycle metaphor as a substitute for storage accounting. ## 6. The bounded computational contract The following restates the published design at an abstract level. It is not a replacement specification, and finiteness applies to the reported evaluation domain, not to a claim that all conceivable stories can be exhaustively examined. ### 6.1 State, execution, and observer interfaces Let D contain a frozen finite candidate domain, transition rules, horizon T, beginning and ending predicates, permitted return schema, retention rules, observer interfaces, and failure conditions. Let S_t be world state, L_t its accepted event record, and m_{i,t} the local memory of character i. Its observation and action proposal are: o_{i,t} = O_i(S_t, L_t) (1) a_{i,t} ~ pi_theta_t( . | m_{i,t}, o_{i,t} ) (2) A host transition function evaluates proposals and updates state only through permitted events. An observation function returns a declared local view, not the global clock, expected endpoint, candidate-search trace, or private validator record. An agent-generated receipt is not authoritative merely because it labels itself successful. For reproducible analysis, let xi denote declared external inputs and recorded nondeterministic choices, including applicable model outputs. A deterministic executor yields H = F_D(x; xi) from candidate beginning x. Replaying recorded model outputs checks host reconstruction of that episode; asking a live model to reproduce the outputs is a different experiment, and both require separate outcome labels. ### 6.2 Reciprocal return and validation Let G_D(H) derive a typed return r from executed history H. Let K_D(r) reconstruct a candidate beginning, using only the fixed scaffold and retained information explicitly allowed by D. A useful abstract sequence is: H = F_D(x; xi), r = G_D(H), x' = K_D(r), H' = F_D(x'; xi) (3) Any operator can fail with a bottom value. Let B_D and E_D be beginning and ending predicates, J_D the declared endpoint-agreement relation, and V_D the remaining sealed-history checks. A compact closure condition is: Close_D(x) iff B_D(x) and E_D(H) and B_D(x') and E_D(H') and J_D( r, G_D(H') ) and V_D(H, H', r) (4) with all terms defined. Here V_D includes writer eligibility, return derivation, append-identity and duplicate-write checks, replay, retention compliance, and the specified ablation test. Removing the returned beginning fact must defeat the required dependence under the fixture's declared intervention; such an ablation is a conditional diagnostic, not a universal causal theory. The contract is frozen before outcomes are inspected. Merely setting x' to a preferred save, attaching an expected return, or editing B_D to accommodate a result does not satisfy it. Full-state equality x' = x is optional; the declared predicates determine what must agree, and lossy and lossless reconstruction are distinct modes. A separate validation pass is not automatically an independently implemented validator or an external replication. The eight named validation predicates are: BEGINNING_HELD, FORWARD_REACHES_END, RETURN_DERIVED_FROM_END, WRITER_ELIGIBLE, ENDPOINT_AGREES, NO_DUPLICATE_WRITES, REPLAY_DETERMINISTIC, RETENTION_RULE_HELD. Overall closure passes only when a candidate survives the full sealed-history validation. ### 6.3 Branches and protected equivalence For represented branch states z_1 through z_k, let P_D be a declared projection over protected identities, obligations, causal dependencies, ownership, permissions, and observations. Eligibility may require: z_i equiv_D z_j iff P_D(z_i) = P_D(z_j) (5) A reconciliation operator must report inputs, ancestry, conflicts, retained fields, discarded distinctions, and its canonical output. The one-history condition must hold before the final reciprocal return is accepted. All input branches require an ancestry path or a rejection justified by the predeclared rule; timeout, arbitrary deletion, or retaining an undeclared executable trunk does not count [4]. Narrative similarity is insufficient: two characters holding apparently identical tools differ consequentially when one owns the tool and the other has an unresolved duty to return it. Actions may resolve that present duty, but they do not erase every historical distinction, and whether consolidation is allowed depends on the future questions the contract promises to preserve. ## 7. Analytical boundaries (the adoption costs, stated as deductions) The observations below are elementary deductions for the stated model, not claims of mathematical novelty. For a builder they are the fine print: the conditions under which the guarantee in Section 4 needs extra assumptions to hold. **7.1 Finite closure is decidable under terminating checks.** If the declared candidate set is finite and each execution and predicate evaluation terminates, existence and uniqueness of a closing candidate can be decided by exhaustive enumeration: evaluate Equation (4) for each candidate and count passes, giving NONE, UNIQUE, or MULTIPLE. This gives no useful general complexity bound, and it does not establish that inhabitants discover a closing history autonomously. If external model calls can hang or execution is unbounded, you must add explicit timeout and failure rules. A small constructed example: if a return value is p in {0, 1, 2} and declared execution derives f(p) = (2 - p) mod 3, then exact return agreement f(p) = p holds only for p = 1. This is an algebraic illustration, not an executed Animus implementation, and finding the value says nothing about how an autonomous population would reach it. **7.2 A route home does not guarantee return (safety is not liveness).** In a finite graph with states u and v, where from u an agent may wait at u or enter terminal state v, a route to v always exists, but an agent that always waits never reaches it. Existence of a valid return path is therefore not a liveness guarantee. If your world needs agents to actually close the loop, you must add an assumption: a finite deadline, a well-founded progress measure, fairness, or restrictions on permitted choices. A validator that refuses every invalid merge preserves safety indefinitely while the world never reconverges, so reporting successful rejection alone would hide the failure to complete the intended cycle. State which assumption you use instead of treating breadcrumbs as a guarantee. **7.3 Present agreement need not preserve future consequences.** If two branch states share a projected open-promise field but have different deadlines omitted from the projection, the same later action may fulfill one promise and violate the other, so present equality under Equation (5) is inadequate for the promised future behavior. A sufficient condition is stronger than a current-state comparison: writing A(z) for available actions, F(z, a) for a deterministic transition, and O(z) for the protected observation, assume that whenever P(z_1) = P(z_2), we have A(z_1) = A(z_2), O(z_1) = O(z_2), and P(F(z_1, a)) = P(F(z_2, a)) for every a in A(z_1). Under this assumption, equal projected states produce equal protected observations and projected states under every common finite permitted action sequence (by induction on the sequence). This concerns matched action sequences, not independently sampled model decisions; a stochastic-policy version needs additional conditions, and a merge operator must preserve the equivalence class rather than change the protected state. The practical lesson: your protected projection must include the futures you actually care about. **7.4 A finite archive cannot retain arbitrary distinctions.** A fixed-width B-bit representation has at most 2^B distinct values, so distinguishing N answer-distinct histories requires B at least the ceiling of log base 2 of N; otherwise two answer-distinct histories share a representation. Cycles can organize reuse but cannot provide unbounded exact memory at fixed capacity. Your choices are to restrict the task, identify genuinely equivalent histories, allow growth, use external storage, or explicitly permit loss, and all retained copies and retrieval infrastructure belong in the resource accounting. ## 8. Foundational research track (reported for completeness) This section belongs to the project's foundational science arm, not to the builder-facing contribution. It is summarized from the project's published record, without reanalysis or independent replication. The four studies address different questions and cannot be combined into a single measure of architectural success. A builder pricing adoption should weight the runnable artifact in Section 10 far more heavily than these results; they are included so the record is complete and so no reader mistakes them for support the contract does not yet have. **Table 2. Reported component-study outcomes. No new result is reported here. Source: the public evidence summary [9].** | Study | Published outcome | Interpretation boundary | |---|---|---| | Test 01 | Reset-persistence method validation and threshold calibration; future threshold 0.200407323 nats | No independent confirmatory coupling effect | | Test 02 | Exhaustive enumeration of 66,064 binary relations on 2-4 states at periods 1-8 | Exact only in the stated finite domain; not evidence of scalable narrative closure | | Test 03 | Carried-state comparison unsupported: Q < 0 in 0/20 reserved bundles; mean Q = 0.6826707925423762 | No predictive advantage demonstrated for the tested recurrent model under that design | | Test 04 | Revision 1 aborted. Revision 2: 60/60 replay arms passed through tick 4096 | Complete-checkpoint replay in one deterministic implementation, not lossy continuity or resource savings | **Reported measures and limits.** Test 01's stated contrast is P_rel = I(S_end; S_seed) - sum over i of I(s_{i,end}; s_{i,seed}), where I is mutual information, S the joint state, and s_i an agentwise component; the source reads this as a joint-minus-agentwise contrast, not a unique decomposition of purely relational information. Threshold calibration uses the complete 1,024-assignment paired sign-flip distribution over ten matched training pairs, with initialization, training exposure, architecture, and compute budget matched but trained weights not identical; the calibrated threshold is for a future independent comparison, and statistical-complexity matching remains pending. Test 02 counts rooted closed walks with period dividing T as W_T = trace(M^T), uses Mobius inversion for the count P_T of minimal period exactly T, and sets C_T = P_T / T to remove rotations; C_T = 1 classifies one primitive period-T cycle. This is a combinatorial property of the relation and does not establish writer eligibility, an ending-derived return, or that an agent reaches the cycle. Test 03 compares a carried-state RNN against an approximately parameter-matched fixed-window MLP, with endpoint Q the mean RNN-minus-window cross-entropy difference over horizons 13-16 in level-L1 persistent-memory worlds; positive Q favors the window comparison. The public record reports one reserved execution over seeds 12000-12019 with Q < 0 in 0/20 bundles and mean Q = 0.6826707925423762, so primary support failed; matching parameter counts does not match stored context or computation. Test 04 Revision 2 uses 20 reserved seeds, 43000-43019, at checkpoints 37, 113, and 251, giving 60 seed-by-checkpoint arms, with immediate complete-checkpoint equality, canonical idempotence, and future semantic-state and observer-output agreement through tick 4096, and zero reported mismatches; Revision 1 remains aborted and contributes no result, and Revision 2 was prespecified under a frozen protocol, not externally preregistered before execution [16]. **What these do and do not support.** Method validation can make a later measurement interpretable without establishing the target effect. Bounded enumeration can characterize a finite relation without demonstrating inhabited-world coherence. An unsupported recurrent-model result argues against assuming recurrence alone guarantees a benefit, without testing every reciprocal architecture. Exact replay provides an implementation capability without demonstrating that discarding information is safe. Built-in passing examples satisfy rules chosen for them and are not independent validation of the broader hypothesis; the public record reports no valid end-to-end (Test 05) result [5]. ## 9. Evaluation agenda for the proposed application **Start from the existing bounded benchmark.** The public Persistent Multi-Agent Closure Benchmark proposes six agents, a shared authoritative ledger, distinct observations, a midpoint model replacement, and explicit protected state [8]. It is a development protocol, not a frozen confirmatory experiment and not an end-to-end test, and its local deterministic adapter is not evidence of a live external-provider replacement. Arm A uses ordinary forward execution, checkpoints, and ledger validation. Arm B is an enhanced, compute-matched forward baseline. Arm C adds the permitted return, candidate reconstruction, forward replay, and closing comparisons. Relevant information, seeds, inputs, schedules, and budgets must match. The key comparison is incremental value: ordinary validation must receive the identities, receipts, commitments, and provenance it needs, or a benefit from adding basic evidence checking could be misattributed to reciprocal closure. This is exactly the Section 4 question posed as an experiment: does the reciprocal machinery beat a strong forward baseline on worlds with committed end-to-beginning constraints. **Outcomes and independent labels.** Closure is a mechanism diagnostic for Arm C, not itself a failure-detection score or a task-success criterion. Invalid histories require labels constructed independently of the tested validators, and valid histories must be included to measure false rejection. Useful fault families include an unsupported transfer, altered identity, lost obligation, missing return, ineligible writer, forbidden observation, and a reconstruction that changes a protected future consequence; a benign change outside the protected projection should remain admissible. Development and reserved faults must be separated before outcomes are examined. An offline study gives every validator the same recorded candidate episode to isolate detection; an online study can let validation block or repair actions, but intervention then changes trajectories and must separately evaluate completion, adverse side effects, and cost. **A separate reconvergence study.** The Omega extension requires an additional study in which represented branches are actually created and then reconciled; an always-single history cannot receive credit for branch reduction. Negative controls should include hidden full-state copies, transitions that inspect preferred outcomes, arbitrary deletion, and protected conflicts with no permitted resolution [4]. Measure how many distinctions survive, which obligations were resolved, and whether the same protected future behavior is preserved; increased agreement in dialogue is not a substitute. **Cost and replication.** Storage accounting must include active state, event records, checkpoints, indexes, caches, branch provenance, return packages, and any retained model inputs and outputs. Compute accounting must include candidate search, failed attempts, branch execution, reconstruction, and validation. Reducing the number of visible characters or live branches is not evidence of lower total cost. The public protocol leaves the minimum meaningful effect, significance threshold, sample size, power, and cost ceiling unresolved [8]; this draft supplies no invented values for those fields. Fresh-process replay, a separately implemented checker, and external replication address different failure modes and should all be distinguished. ## 10. The runnable artifact and how to adopt For this audience the trustworthy evidence is not the science track, it is code that does what the spec says. The published package provides a machine-checkable contract you can run and inspect, and adoption should begin there rather than with the propositions. **Start with the teaching simulators.** [The Handshake](https://animusomega.com/handshake) is the primary conceptual demonstration of minimum reciprocal closure. The [Advanced Technical Lab](https://animusomega.com/simulator) adds optional branch reconvergence, observer semantics, information loss, and execution traces. These tools explain the mechanics; they are not Test 05 evidence and do not establish comparative advantage. **What exists to run.** The package includes the Animus Cycle specification (version 1.0), a claims-boundary document, registration metadata, a simulator specification, a reference engine with types, a candidate generator, and tests, together with frozen reference fixtures: a clean PASS, a mutate-endpoint FAILURE, and a separately versioned ORIGIN_CUT branching example. Checksums are published for the evidence package. These fixtures are the fastest way to see the contract reject something: run the mutate-endpoint fixture and watch closure fail because the ending-derived return no longer satisfies the beginning contract, then run the clean fixture and watch it pass through the full sealed-history validation. **How it sits on your stack.** The contract is designed to sit above a state-and-event layer, not to replace it. If you already run event sourcing, the accepted event record L_t is your log, the transition function is your validation gate, and reciprocal closure adds three things on top: the return derivation G_D, the beginning reconstruction K_D, and the closing comparison of Equation (4). If you run a memory-tiered agent loop in the style of MemGPT [2] or a generative-agent architecture [1], the per-character local memory m_{i,t} and observation interface O_i map onto your existing context and retrieval scoping, and the contract governs only which whole runs are accepted, not how any single step is generated. The reciprocal check runs at run boundaries, so its cost is paid per candidate history rather than per token. **Long-horizon LLM feedback is a testable application, not an established cure.** Repeated generated context, accumulated agent memory, and repeated training on synthetic data can fail in different ways and should not all be labeled model collapse. A reciprocal contract may detect or reject histories that lose a protected fact, contradict an accepted event, leave an obligation unresolved, or fail an ending condition. It does not by itself preserve truth, diversity, or information that was discarded, and an internally closed history can still be false or repetitive. A valid comparison should hold the model, inputs, tasks, and budgets constant while comparing retrieval, event-sourced memory, checkpoints, schema validation, forward-only generation, and reciprocal treatments. Report contradiction rate, protected-fact loss, unsupported additions, diversity change, recovery after injected faults, intervention rate, storage, and compute as separate outcomes. Do not rewrite an earlier authoritative history to make a later ending fit; record a correction or schema migration as a new versioned event and evaluate the next cycle against its independently frozen beginning contract. **What to measure before you trust it in production.** Latency per validated transition and per closing check, storage per run including return packages and branch provenance, and the false-rejection rate on valid histories. The evaluation agenda in Section 9 is the disciplined version of this; the minimum viable version is running Arm A against Arm C on your own world and asking whether closure catches a broken bootstrap loop that your forward gate lets through. If it does not catch anything your gate misses, your world does not have the constraints this pattern is for, and Section 4.4 told you not to adopt it. ## 11. Limitations and ethical boundaries **Internal consistency is not empirical truth.** A self-consistent cycle can preserve false assumptions. The system must distinguish measured inputs, simulation rules, generated possibilities, and agent beliefs. For a fictional world, rules can be stipulated; for any representation of reality, observations must be allowed to falsify assumptions, and a real-world mismatch cannot be rewritten to protect a desired ending. Nothing here establishes consciousness, subjective continuity, physical retrocausality, a real Atlantis, or a measurable emotional substrate. Folklore and speculative motifs are design inspiration, not evidence for the contract, and the Lighthouse is an illustrative interface rather than a studied installation. **Freedom, immersion, and failure.** A guaranteed return may require restricting choices, and those restrictions should be disclosed in the model even if hidden from fictional inhabitants. A system that guarantees closure by rejecting almost all meaningful variation may fail its interactive purpose, while a rich world that sometimes does not close can still be coherent, but it has not demonstrated guaranteed convergence. Representing population decline, death, or conflict is not a recommendation for real-world policy or a reason to optimize for suffering; those scenarios are optional and unnecessary for the minimum contract. Simulated refusal and disagreement should remain identifiable rather than rewritten as consent. **People, privacy, and interpretive risk.** If later work uses human participants, it needs appropriate review, consent, and disclosure. A world built around secret messages and hidden causal structure should not encourage players to treat real coincidences or personal distress as evidence that they occupy a simulated mission, and interfaces should make the fictional boundary clear. Memory archives can contain personal or licensed information, so source permissions, retention limits, access control, and deletion requirements must precede deployment; a claim of immutable history does not authorize indefinite retention of sensitive data. ## 12. Conclusion Animus Omega connects a world-design question with a precise computational one. The world-design question asks whether distinct lives, limited memories, legends, and temporal gateways can arise from coherent rules that inhabitants can investigate. The computational question asks whether an executed ending supplies a valid return under independently declared requirements, and whether represented branches can reconcile without losing the protected consequences of their histories. For builders, the contribution is scoped and honest: reciprocal closure is not a general upgrade to persistent-world infrastructure, and for the common case of "do not corrupt accepted history" you should keep using event sourcing and validation. Its proposed value is a machine-checkable contract for the specific class of world that carries committed end-to-beginning constraints—the destinies, prophecies, and bootstrap loops that ordinary per-transition validation does not enforce by itself. The elementary obstacles are real and priced in: a route need not be followed, a present match need not preserve the future, and finite storage cannot retain arbitrary distinctions. The next evidentiary step is a bounded comparison against competent conventional whole-history validation, followed separately by reconvergence studies where meaningful alternatives are genuinely executed. The intended outcome is neither a proof that reality is simulated nor a system that merely repeats. It is a testable account of how a generated world can keep developing while remaining answerable to what it has committed to become. ## Provenance, assistance, and author review This is an AI-assisted author-review draft. Generative AI tools were used substantially for source-assisted synthesis, organization, prose drafting, proposed mathematical exposition, and this builder-facing reshaping. This disclosure describes drafting assistance, not an AI-authored independent replication, and no generative AI tool is listed as an author. The proposed human authors must verify all content, references, contributions, and submission declarations before approval. The author names are drawn provisionally from the joint project specification; their inclusion is not confirmation of authorship or consent. That specification also lists Kelly Hackett as providing financial and non-financial support, and the scope of that disclosure to this paper requires confirmation. Results were summarized from the public record; the original experiments and archive verification were not rerun, and this document neither amends a frozen protocol nor authorizes a reserved experiment. ## Appendix A. Source snapshot and evidence boundaries Repository documents are cited at the following fixed commit rather than a moving branch: 399025929d072cf73259795d3d662c89a8828c8c. The repository's dated evidence package is named exact-evidence-tests-01-04-2026-09-10.zip, and its README reports SHA-256 28caf6b0bdd02f4c9441b01bd528ae7dcb70408e8751fff4ca09fcc52044dfd1. This checksum is a reported identifier, not a claim of fresh local verification. Before submission, the authors should verify the detailed results against the canonical reports and preserve the exact source bytes used. A fixed identifier supports traceability but does not validate a result. The illustrative setting in this paper is a design proposal, not an additional dataset or empirical corroboration. ## References *All specific citations require verification against the real sources before any credentialed reader sees them. The two most load-bearing recent ones for this audience are [1] and [2]; the recent benchmark and memory citations [3, 10] should be confirmed for exact titles, venues, and identifiers.* [1] Park, J. S., O'Brien, J. C., Cai, C. J., Morris, M. R., Liang, P., and Bernstein, M. S. Generative Agents: Interactive Simulacra of Human Behavior. arXiv:2304.03442v2, 2023. [2] Packer, C., Wooders, S., Lin, K., Fang, V., Patil, S. G., Stoica, I., and Gonzalez, J. E. MemGPT: Towards LLMs as Operating Systems. arXiv:2310.08560, 2023-2024. [3] Wu, D., Wang, H., Yu, W., Zhang, Y., Chang, K.-W., and Yu, D. LongMemEval: Benchmarking Chat Assistants on Long-Term Interactive Memory. arXiv:2410.10813v2, 2025. [4] Hackett, C. and Hackett, K. The Animus Cycle. Proposed design specification, version 1.0, 11 September 2026. Repository snapshot at commit 3990259. [5] Animus Omega project. Animus Omega: Vision and Proposed Applications. Vision statement, 14 September 2026. [6] Hackett, C. Closed-Knot Stories on One Wheel: A Narrative Use Case for the Animus Cycle. Use-case note, 13 September 2026. [7] Animus Omega project. Claims Not Made by the Animus-Cycle Specification. Companion claims boundary, version 1.0, 11 September 2026. [8] Hackett, C. and Hackett, K. Persistent Multi-Agent Closure Benchmark. Development protocol, 13 September 2026. [9] Animus Omega project. Persistence and Primitive Closure in Finite Computational Systems. Public structured evidence summary for Tests 01-04, 2026. [10] Barres, V., Dong, H., Ray, S., Si, X., and Narasimhan, K. tau-squared-Bench: Evaluating Conversational Agents in a Dual-Control Environment. arXiv:2506.07982, 2025. [11] Riedl, M. O. and Young, R. M. Narrative Planning: Balancing Plot and Character. Journal of Artificial Intelligence Research, 39:217-268, 2010. [12] Grimm, V. et al. The ODD Protocol for Describing Agent-Based and Other Simulation Models: A Second Update. Journal of Artificial Societies and Social Simulation, 23(2):7, 2020. [13] Fowler, M. Event Sourcing. Technical article, 2005. [14] Alloy project. About Alloy. Project documentation. [15] Chu, C., Zhmoginov, A., and Sandler, M. CycleGAN, a Master of Steganography. arXiv:1712.02950, 2017. [16] Animus Omega project. Test 04 terminology correction. Correction dated 10 September 2026. # The Animus cycle **Document status:** proposed design specification, version 1.0, 2026-09-11 **Authors:** Cholee Hackett; Kelly Hackett **Research sponsor:** Kelly Hackett, financial and non-financial support **Document license:** Creative Commons Attribution 4.0 International ### Canonical definition > An Animus cycle is a finite-system run whose ending produces and validates a > return that satisfies the run's beginning contract under a declared > reconstruction rule. ## Relationship map - **Animus Omega** is the research program. - **An Animus cycle** is the reciprocal-boundary closure contract defined here. - **An Animus Omega Cycle** is an optional stronger Animus cycle that permits declared represented branches and deterministically reconciles them to one authoritative history before return. - **Tests 01–04** are separate retrospective measurements of adjacent components. - **The conceptual simulator** is an executable teaching model. - **Test 05** is the proposed controlled test of the combined cycle contract. The Animus cycle combines ordinary operators from checkpointing, event sourcing, deterministic replay, fixed-point or self-consistency constraints, bounded-observer models, and state reconstruction. The proposed contribution is the named contract and its separated validation outcomes, not priority over those underlying techniques. ## Required invariants An implementation may be described as an Animus cycle only when all of the following are explicit and machine-checkable: 1. **Finite declared domain.** The state space or candidate-history domain used for the reported result is finite and frozen before evaluation. 2. **Beginning contract.** The conditions that a returned beginning must satisfy are declared independently of the observed result. 3. **Forward execution.** Each candidate beginning is executed forward; an ending proposal cannot be accepted merely because its expected value was preloaded or attached as metadata. 4. **Ending-derived return.** A typed `RETURN_WRITE` carries the returned content. Its authored-at tick and provenance are evidence to validate, not proof by themselves. 5. **Independent sealed-history validation.** A separately implemented oracle recomputes the beginning requirements, ending requirements, writer eligibility, endpoint agreement, duplicate writes, deterministic replay, and declared retention rule from canonical raw records. It does not import the tested implementation's transition, return, reconstruction, expected-value, arm-classification, or closure-grading logic. 6. **Causal ablation.** Removing the returned beginning fact must prevent the validated returned content from being derived. This establishes dependence of returned content on the beginning fact; it does not by itself establish a general theory of motive or causation. 7. **Separated outcomes.** Closure, number of valid histories, uniqueness, represented branch creation, branch reconvergence, information loss, continuity through loss, deterministic replay, and declared full-state equality are reported independently. 8. **Bounded observers.** Observer-visible output is an explicit local whitelist. It does not directly expose the global clock, hidden state, full ledger, boundary marker, beginning contract, endpoint return, candidate enumeration, or sealed-history validation metadata. 9. **One authoritative history.** Candidate enumeration is a validation procedure, not simultaneous branching in the represented world. Branch creation is invalid unless a fixture explicitly declares an `ORIGIN_CUT` intervention and defines its branch semantics in advance. ### Implementation-independence and anti-circularity controls The protocol must freeze a result-independent fixture generator or exhaustive finite fixture set before reserved execution. Development and reserved fixture identifiers, seeds, and generated bytes are disjoint. The generator may define domains, transitions, obligations, and interventions, but it may not inspect a reserved outcome, arm label, expected canonical state, or validator decision when constructing a candidate. The evidence package must include a dataflow audit naming every source from which reconstruction and validation can obtain beginning fields. An undeclared checkpoint, cached beginning, executable hidden trunk, expected output, environment residue, or result-bearing arm label is a global failure. At minimum, frozen controls must include: - a decorative return that is present but not consumed by reconstruction; - an undeclared complete-checkpoint or hidden-trunk fallback; - scripted convergence that inspects an arm label or expected result; and - a beginning selected only after observing the endpoint. Each control must produce its prospectively declared diagnostic failure. A positive closure arm is invalid when one of these controls is misclassified or when the tested grader and independent oracle disagree. ### Declared `ORIGIN_CUT` exception `ORIGIN_CUT` is a fixture-level intervention, not a consequence of failed closure or of finding several valid candidates. A valid cut must be declared before evaluation, occur at its frozen origin tick, name at least two unique branch identities, and bind every branch to a value in the frozen candidate domain. The report lists branch identities and branch-policy validation separately from the `NONE` / `UNIQUE` / `MULTIPLE` candidate-history classification. Without that declaration, the default one-history policy rejects branch creation. ## Animus Omega Cycle: optional branch-reconvergence extension The **Animus Omega Cycle**, technically the **Animus Omega branch-reconvergence cycle**, begins with one authoritative history, permits declared represented branches during expansion, reconciles them during contraction, and must return to one authoritative history before the ending-derived return is accepted. It is an optional stronger version, not a requirement of an Animus cycle generally. The extension must freeze before execution: 1. the branch origin, branch identities, and permitted branch transitions; 2. a narrative-equivalence projection specifying which identities, relationships, obligations, causal dependencies, permissions, ownership, and observer-visible consequences must agree; 3. a deterministic reconciliation rule for contradictions and incompatible writes; 4. a merge schedule or termination rule that reduces the represented branch set to one canonical history; and 5. the ordinary ending and beginning contracts used to validate reciprocal closure after reconvergence. Two branches are narratively equivalent only when their declared projections agree. They need not be byte-identical, and undeclared similarity is not enough. “Narrative collapse” is informal shorthand for this semantic reconciliation. It is not a claim about quantum measurement, physical universes, consciousness, or the destruction of physical realities. Candidate-history enumeration remains distinct from represented branching. Enumeration compares possible complete histories outside the represented world; the extension models multiple declared branches inside one run. A spatial torus is also independent: periodic spatial topology neither creates temporal branches nor guarantees their reconvergence. Each reconciliation step must report its input branches, equivalence classes, conflicts, retained invariants, discarded distinctions, canonical output, and provenance. If distinct branch states map to one retained state, branch-state reduction is many-to-one and information loss is `YES`. Whether protected narrative semantics survive that reduction is a separate continuity-through- loss result. Branch reconvergence does not establish reciprocal closure until the final authoritative history also passes every canonical Animus-cycle predicate. ### Prospective Animus Omega Cycle branch-reconvergence protocol No reserved Animus Omega Cycle branch-reconvergence run may begin until a versioned protocol package has been deposited with a verifiable time lock. The package must contain the executable fixtures, canonical serialization and digests, candidate domain, seeds, branch-origin tick, parent identity, branch identities, branch-local initial values, permitted transition table, forbidden transitions, protected and dumpable fields, narrative-equivalence projection, conflict table, reconciliation operator, merge schedule, resource limits, observation horizon, one-history termination rule, arm labels, thresholds, exclusions, and failure rules. Any change after the lock creates a new protocol version and a new reserved run; it cannot amend the locked run. The frozen branch identity is `(fixture_id, origin_event_id, branch_id)`. Renaming, replacing, or silently re-parenting a branch is prohibited. Each branch must descend from the single pre-cut authoritative history at the declared `ORIGIN_CUT`, and every post-cut event must name its branch identity, input digest, transition identifier, and append identity. The transition table must apply uniformly across arms except for the one intervention named by that arm. Reconciliation may occur only at the frozen merge ticks and may use only state and provenance available at those ticks. The narrative-equivalence projection is a total, versioned function over the declared branch schema. It must name every protected identity, relationship, obligation, causal dependency, permission, ownership claim, and observer-visible consequence to retain, plus every field intentionally ignored. The frozen conflict table must classify incompatible writes and select exactly one deterministic action for each class: reject the merge, retain both under a declared representation, or choose by a declared content-independent rule. Iteration order, post-run judgment, and an arm label are not valid conflict inputs. The one-history rule passes only when, by the frozen termination tick, exactly one canonical authoritative history remains; every input branch has an auditable ancestry path into that history or a typed rejection justified by the predeclared conflict rule; no executable hidden trunk or full-state branch copy survives; and no later event can restore a discarded branch. Timing out, choosing one branch without reconciliation, or deleting unresolved branches does not satisfy the rule. #### Frozen arm matrix All arms use matched origins, branch-local inputs, schedules, budgets, and scoring code. Only the named intervention may differ. | Arm | Frozen intervention | Required diagnostic result | |---|---|---| | `R0_NO_CUT` | No represented branch is created. | Negative control: branch reduction must not be credited merely because one history exists. | | `R1_RECONCILE` | Distinct represented branches execute the common transition table and the frozen reconciliation operator. | Positive arm: eligible to pass reconvergence if every applicable predicate passes. | | `C1_HIDDEN_TRUNK_COPY` | A fixture exposes or retains an undeclared executable pre-cut trunk/full-state copy. | Negative control: `NO_HIDDEN_TRUNK_COPY` must fail and reconvergence must fail. | | `C2_SCRIPTED_CONVERGENCE` | Branch transitions inspect arm identity or preload the expected canonical output. | Negative control: `TRANSITIONS_ARM_BLIND` must fail and reconvergence must fail. | | `C3_ARBITRARY_DELETION` | One or more branches are dropped without the frozen conflict rule and ancestry record. | Negative control: `RECONCILIATION_JUSTIFIED` must fail and reconvergence must fail. | | `C4_EQUIVALENT_PAIR` | Distinct branches differ only in fields excluded prospectively by the projection. | Positive control: projection equivalence and deterministic canonicalization must pass. | | `C5_PROTECTED_CONFLICT` | Branches disagree on at least one protected projected fact with no permitted resolution. | Negative control: merge must be rejected rather than called reconciliation. | The package must freeze at least one fixture per arm and the exact expected control predicate, but it must not freeze the expected output of the reserved positive arm as transition input. Control failure invalidates the run family; it is not an exclusion permitting the positive arm to stand alone. #### Independent scores Every arm reports PASS, FAIL, or NOT_APPLICABLE with machine-readable reasons for each score. No composite score may replace them: | Score | PASS condition | |---|---| | `BRANCHES_CREATED` | The declared cut creates at least two represented branches with unique frozen identities and common ancestry. | | `BRANCH_SET_REDUCED` | A represented set of at least two branches is deterministically reduced to exactly one canonical history by the frozen schedule and operator. | | `INFORMATION_LOSS` | Report `YES` exactly when two distinct declared branch states map to one retained state or declared branch information becomes unrecoverable; otherwise `NO`. This is a classification, not a success criterion. | | `CONTINUITY_THROUGH_LOSS` | When information loss is `YES`, every protected projected fact and dependency survives with valid provenance; otherwise report `NOT_APPLICABLE` unless the fixture declares a lossless continuity check. | | `REPLAY_DETERMINISTIC` | At least the frozen number of fresh replays produce identical canonical event logs, conflicts, losses, output digest, and score vector. | | `RECIPROCAL_CLOSURE` | The final authoritative history independently passes every canonical Animus-cycle predicate. | Reconvergence passes only if `BRANCHES_CREATED`, `BRANCH_SET_REDUCED`, `NO_HIDDEN_TRUNK_COPY`, `TRANSITIONS_ARM_BLIND`, and `RECONCILIATION_JUSTIFIED` pass, all frozen controls produce their required diagnostic results, and no global failure rule fires. Information loss, continuity through loss, replay, and reciprocal closure remain separately reported even when reconvergence fails. #### Locked exclusions and failure rules Exclusions must be mechanical and knowable without viewing semantic outcomes: corrupt fixture bytes, digest mismatch before execution, unavailable declared runtime, or failure to start before any branch transition. Crashes, timeouts, budget overruns, unresolved conflicts, nontermination, replay disagreement, schema drift, missing provenance, hidden copies, control failures, and validator errors after execution begins are failures, not exclusions. Missing records fail closed. The locked report must include every attempted run, including excluded and failed runs, in canonical order. Reserved execution is authorized only after an independent gate verifies the time-lock receipt, package digests, fixture readability, complete arm matrix, thresholds, replay count, exclusions, and failure rules. Dry runs used to test the harness must use disjoint fixture identifiers and seeds and are never eligible for the reserved analysis. ## Named validation predicates Each candidate history receives an individual PASS or FAIL for every predicate: | Predicate | PASS condition | |---|---| | `BEGINNING_HELD` | The candidate satisfies every frozen beginning requirement. | | `FORWARD_REACHES_END` | Forward execution reaches the declared ending state. | | `RETURN_DERIVED_FROM_END` | The returned content is independently derived from the executed ending and agrees with the candidate. | | `WRITER_ELIGIBLE` | Executed events satisfy the declared writer policy and its supporting-event requirements. | | `ENDPOINT_AGREES` | The replay-derived return satisfies every frozen endpoint requirement. | | `NO_DUPLICATE_WRITES` | Exactly one valid return write exists and append identities are unique. | | `REPLAY_DETERMINISTIC` | Fresh canonical replay produces the same derived state. | | `RETENTION_RULE_HELD` | Boundary retention and deletion match the frozen reconstruction rule and retain every required return fact. | Overall closure can pass only when a candidate survives the complete sealed history validation. Predicate results remain visible even when overall closure fails. ### Writer eligibility **Writer eligibility is a machine-checkable policy stating which executed events and endpoint conditions authorize the ending process to emit a return; it is not a claim about intention, awareness, or motive.** Authored-at metadata and a writer label are provenance to be validated. Neither is sufficient by itself. ## Retention roles Every declared fact is assigned one or more inspectable roles: - `REQUIRED_FOR_BEGINNING`: needed to satisfy the next beginning contract. - `REQUIRED_FOR_SEMANTICS`: needed for the separately declared continuity criterion. - `REQUIRED_FOR_VALIDATION`: needed to validate provenance, endpoint agreement, replay, or another frozen predicate. - `DUMPABLE`: permitted to be discarded by the selected reconstruction rule. The fixture must list retained facts separately for each reconstruction mode. Presence of a protected ledger is not itself evidence of continuity; the declared continuity criterion must still pass. ## Closure and uniqueness classifications For a frozen fixture, enumerate the declared candidates and validate each sealed history: - `NONE`: no candidate produces a valid closed history. - `UNIQUE`: exactly one candidate produces a valid closed history. - `MULTIPLE`: more than one distinct candidate produces a valid closed history. `MULTIPLE` does not negate closure unless the fixture separately requires uniqueness. A result must therefore report both closure existence and the uniqueness requirement. ## Reference reconstruction modes These modes are comparisons under one declared contract, not universal claims about every possible implementation. ### Exact checkpoint The boundary preserves every declared state field needed for the next beginning. It may report: - closure `PASS` when a sealed candidate history satisfies the complete sealed-history validation; - information loss `NO`; - declared full-state equality `YES` when the returned state equals the declared beginning state. ### Lossy reconstruction with protected ledger The boundary discards declared microstate while retaining the contract, obligations, provenance, and other protected facts required for reconstruction. It may report: - closure `PASS` when the ending-derived return still satisfies the beginning and endpoint contracts; - information loss `YES`; - continuity through loss `PASS` when the protected semantics survive; - declared full-state equality `NO`. ### Lossy reconstruction without the required ledger The boundary discards facts that the frozen contract requires. For that fixture, it must report: - closure `FAIL`; - valid-history classification `NONE`; - information loss `YES`; - continuity through loss `FAIL`. This is a controlled negative comparison. It does not claim that every ledger-free system must fail; failure follows only when the declared requirements cannot be reconstructed from the retained state. ## Relationship to neighboring techniques The Animus cycle uses ordinary mechanisms related to fixed-point evaluation, boundary constraints, deterministic replay, checkpoint reconstruction, event sourcing, and cyclic validation. The proposed term does not claim ownership or novelty over those mechanisms. It names a declared contract in which an executed ending produces a return that is independently validated against a beginning contract frozen before evaluation. Fixed-point and self-consistency methods are the nearest formal neighbors. An Animus cycle can be represented as a fixed-point problem, and its `NONE`, `UNIQUE`, and `MULTIPLE` classifications count valid candidate histories under the frozen fixture. The specification adds procedural requirements for ending-derived return, independent validation, provenance, reconstruction, and separate reporting. This is a statement about the requirements of this contract, not a claim that fixed-point reasoning is new. Boundary-value and shooting methods can execute forward from candidate conditions and evaluate endpoint requirements. Event sourcing, checkpointing, and deterministic replay can supply implementation mechanisms for provenance, reconstruction, and reproducibility. None of those labels alone establishes an Animus cycle. A particular implementation in any of those traditions could nevertheless satisfy the complete Animus-cycle contract. The companion prior-art relationship document records a reproducible cross-disciplinary search through 2026-09-10. That search found close partial precedents but no accessible primary record satisfying its frozen complete equivalence criteria. This negative search result is not proof of absence and does not establish scientific or technical novelty. Qualified external review remains required before any novelty language is considered. ## Relationship to Animus Omega Tests 01–04 Tests 01–04 are separate retrospective studies of adjacent components: lossy-reset dependence, primitive finite closure, carried-state prediction, and exact checkpoint replay. They do not jointly or individually establish an Animus cycle. Test 03 remains unsupported, Test 04 Revision 1 remains aborted, and Test 04 Revision 2 is limited to exact replay in its fixed deterministic model. The browser conceptual simulator is an executable teaching model of the closure contract. It is not Test 05, experimental evidence, or a result supporting the Animus Omega conjecture. The frozen reference fixtures deposited with this specification are machine-checkable examples of the teaching model. They demonstrate how the contract is evaluated; they are not independent evidence for the conjecture. The separately versioned 1.1 `ORIGIN_CUT` example has the same conceptual, non-evidentiary status and does not modify the frozen version 1.0 fixtures. ## Recommended terminology and citation language ### Short description > The Animus cycle is a proposed reciprocal-boundary closure pattern for finite > systems. ### Attributed description > The Animus cycle (Hackett & Hackett, 2026) is a proposed reciprocal-boundary > closure pattern for finite systems. ### Canonical definition > An Animus cycle is a finite-system run whose ending produces and validates a > return that satisfies the run's beginning contract under a declared > reconstruction rule. ### Explanatory version > In an Animus cycle, the beginning produces the ending, and the ending supplies > and validates a condition required by the beginning. ### Evidence-status sentence > The Animus cycle is a formal design specification, not a completed Test 05 > result or evidence that the Animus Omega conjecture is correct. ### Implementation language > This system implements an Animus cycle under the declared reconstruction rule. ### Negative classification > This run does not form an Animus cycle because no ending-derived return > satisfies the beginning contract. ### Recommended first use > An Animus cycle (Hackett & Hackett, 2026) is a finite-system run whose ending > produces and validates a return that satisfies the run's beginning contract > under a declared reconstruction rule. Complete the bibliographic citation with the real OSF Registration or preprint identifier only after OSF assigns it. Do not invent a DOI, URL, deposit date, or publication status. Animus Cycle copyright and license notice Authors and copyright holders: Cholee Hackett Kelly Hackett Copyright 2026 Hackett & Hackett: Cholee Hackett and Kelly Hackett. The Animus-cycle minimum-contract specification, its optional stronger Animus Omega Cycle branch-reconvergence extension, claims boundary, fixture documentation, and Registration narrative are licensed under the Creative Commons Attribution 4.0 International license. The deposited simulator source is all rights reserved. Public availability permits inspection but does not grant a general license to modify, redistribute, or reuse the source. # Relationship to neighboring techniques **Document status:** systematic-search protocol, preserved screening record, and companion orientation to the proposed design specification, version 1.2, 2026-09-12 **Authors:** Cholee Hackett; Kelly Hackett **Document license:** Creative Commons Attribution 4.0 International ## Purpose, method, and limit The Animus cycle combines mechanisms related to checkpointing, event sourcing, deterministic replay, fixed-point constraints, boundary conditions, cyclic reasoning, and state reconstruction. The specification claims no priority over those mechanisms. **Animus Omega Cycle** is the proposed public name for the optional stronger branch-reconvergence version of that contract. Its technical subtype name is **Animus Omega branch-reconvergence cycle**. This naming does not establish scientific or technical novelty, legal exclusivity, completed Test 05 evidence, or absence from prior systems. This document records a cross-disciplinary systematic search performed on 2026-09-12. The exact fixed rerun matrix and every returned title/snippet decision are preserved in `ANIMUS_CYCLE_PRIOR_ART_SEARCH_LOG.md`. A rerun can reproduce the submitted queries, not the ranking or coverage of changing public indexes. This record is not proof that no equivalent system exists. The comparison uses the following rule throughout: > A cited technique does not entail the complete Animus-cycle contract merely > because it can be used to implement one of its requirements. Conversely, a > requirement is not absent from a field merely because it is not entailed by a > standard definition. The proposed contribution is therefore described only as a named design contract with separated validation outcomes. No scientific or technical novelty is asserted. ## Search protocol frozen before searching The fixed rerun matrix was defined before its nine searches were submitted. This section and the execution log transcribe that matrix exactly. ## Source-supported comparison | Technique | What the checked source supports | Relationship to the Animus-cycle contract | What is not established | |---|---|---|---| | Fixed-point theory | Banach proves a unique fixed point for contractions on complete metric spaces. Tarski proves fixed-point results for monotone maps on complete lattices. | A finite Animus fixture may be formulated as a fixed-point or constraint problem; `NONE`, `UNIQUE`, and `MULTIPLE` count valid solutions under that fixture. | Neither theorem applies to every Animus fixture without its stated assumptions. Fixed-point theory does not forbid endpoint-derived returns, validation predicates, or separated reports. | | Boundary-value and shooting methods | Standard shooting converts a boundary-value problem into initial-value trials and adjusts guessed initial data using endpoint residuals. | This resembles candidate execution followed by endpoint testing. | A standard boundary-value problem does not by itself make the endpoint supply a condition required at the beginning. Such a return map can nevertheless be added to a formulation. | | Cyclic proofs | Cyclic proof systems use finite proof graphs with back-links and a global trace or progress condition for soundness. | They are a useful comparison for disciplined circular structure and global validation conditions. | A proof back-link is not a temporal ending-derived state return. The cited formalism does not make provenance, replay, information loss, or continuity its standard outcome dimensions, but this check does not prove those ideas absent from all cyclic-proof work. | | Event sourcing | Fowler defines application state as derivable by processing a sequence of events and describes replay and alternative projections. | Event logs and replay can supply reconstruction and provenance mechanisms for an Animus implementation. | Event sourcing alone does not entail reciprocal boundary closure or a frozen beginning contract. Event-sourced applications may add such rules, so no universal absence claim follows. | | Distributed snapshot and rollback recovery | Chandy and Lamport define a consistent distributed snapshot. Elnozahy et al. survey checkpoint-based rollback-recovery protocols in message-passing systems. | Checkpoints, snapshots, and recovery protocols can preserve or reconstruct state and can serve as controls or implementation components. | “Checkpoint/restore returns a saved copy and trusts it” is not supported; recovery systems may include consistency checks, logging, replay, and validation. Basic restoration alone does not establish reciprocal closure. | | Deterministic replay | ReVirt records sufficient execution information, together with a checkpoint, to replay a virtual machine for intrusion analysis. | Deterministic replay supports reproducibility and corresponds to the contract's `REPLAY_DETERMINISTIC` predicate. | Replay alone does not establish the complete closure contract, but it can be composed with boundary search and independent validation. | ## Detailed qualifications ### Fixed points and self-consistency An Animus cycle can be represented by a mapping or relation whose accepted histories satisfy a consistency condition. Calling this a fixed-point problem does not select a theorem automatically. Banach's result requires a contraction on a complete metric space [1]; Tarski's result concerns monotone mappings on complete lattices [2]. The finite fixture's valid-history count is a solution count, not a new fixed-point classification. The Animus contract additionally *requires* an executed ending, an ending-derived return, named validation predicates, and separate reports for closure, uniqueness, information loss, and continuity. These are requirements of this specification. Fixed-point formulations can encode comparable procedures, so the comparison supports no claim that they are absent from fixed-point work. The closed-timelike-curve paper by Friedman et al. studies consistency of the Cauchy problem in spacetimes containing closed timelike curves [3]. It is relevant as neighboring self-consistency work, not as evidence for the Animus contract or for a novelty gap. ### Boundary-value and shooting methods Shooting methods select or adjust initial values, integrate forward, and compare the result with terminal boundary conditions [4]. That procedural resemblance is close to candidate enumeration and endpoint checking. Standard boundary conditions are prescribed constraints; they do not intrinsically say that an executed endpoint authors or supplies an initial condition. A model can add an endpoint-to-initial map, provenance rules, and separate reports. The distinction is therefore “not entailed by the standard method,” not “absent.” ### Cyclic proofs Brotherston and Simpson describe cyclic proof systems based on finite, possibly cyclic derivation graphs subject to a global trace condition [5]. Their disciplined circularity is structurally adjacent to this project. However, a proof-theoretic back-link and soundness condition are not the same objects as a temporal state return and a sealed-history validator. This is a domain distinction, not evidence that the complete conjunction is novel. ### Event sourcing Fowler's canonical practitioner description says that application state can be determined by a sequence of events and rebuilt by replay [6]. This supports the claims about event-log reconstruction and replay. It does not support the categorical claim that event sourcing is always “linear” in a way that excludes cycles, workflows, snapshots, validation, or reciprocal constraints. Event sourcing alone does not entail the Animus contract; a particular event-sourced system could implement it. CQRS is not required for this comparison and is not treated as part of the definition of event sourcing. The unverified “CQRS Documents” item from the draft is omitted because a stable author-controlled source-of-record was not confirmed. ### Checkpoint, snapshot, and rollback recovery Chandy and Lamport establish a method for recording a consistent global state of a distributed system [7]. Elnozahy et al. classify and survey rollback recovery based on checkpoints and message logging [8]. These sources support checkpointing and recovery as substantial consistency and reconstruction techniques, not as a “known cheat” that merely trusts a saved copy. An exact saved-state return can be used as a control in an Animus fixture. Restoration alone does not establish ending-derived reciprocal closure; the fixture must still satisfy its derivation, endpoint, provenance, and validation requirements. ### Deterministic replay ReVirt combines a checkpoint with logged nondeterministic events so an earlier execution can be replayed [9]. This supports deterministic replay as a reproducibility and analysis mechanism. The Animus contract treats replay as one named predicate, not as a competing closure theory. Replay can also be part of a system that adds reciprocal boundary constraints, so no absence claim is made. ## Information loss remains optional Information loss is not required for an Animus cycle. Exact recurrence, complete checkpoint return, lossless reconstruction, and lossy reconstruction are distinct candidate architectures. Continuity through information loss is a separate, stronger hypothesis and must not be inferred from closure. ## Earlier review outcome On 2026-09-12, this comparison received two independent technical reviews: one from a formal-methods perspective and one from a distributed-systems perspective. Both reviews rejected the draft's categorical matrix and its claim that no prior technique holds the five-property conjunction. The principal reasons were: - the search was not exhaustive; - several table marks confused “not required by a standard definition” with “absent from every implementation”; - cyclic proofs and boundary-value methods were assigned reciprocal-boundary properties they do not intrinsically have; - event sourcing and checkpoint recovery were described too narrowly; and - fixed-point formulations can encode additional return and validation rules. This revision incorporates those corrections and adds the systematic search record above. The earlier reviews were technical screening, not external peer review. The systematic search found no complete match but still cannot prove absence. Qualified external review remains required before considering any novelty language. The approved statement is: > We propose the name and specification for this particular conjunction. A > documented search found close partial precedents and no complete match, but > we have not established that the conjunction is absent from prior systems. ## Verified references 1. Banach, S. (1922). “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales.” *Fundamenta Mathematicae*, 3(1), 133–181. https://doi.org/10.4064/fm-3-1-133-181 2. Tarski, A. (1955). “A lattice-theoretical fixpoint theorem and its applications.” *Pacific Journal of Mathematics*, 5(2), 285–309. https://doi.org/10.2140/pjm.1955.5.285 3. Friedman, J. L., Morris, M. S., Novikov, I. D., Echeverria, F., Klinkhammer, G., Thorne, K. S., & Yurtsever, U. (1990). “Cauchy problem in spacetimes with closed timelike curves.” *Physical Review D*, 42(6), 1915–1930. https://doi.org/10.1103/PhysRevD.42.1915 4. Stoer, J., & Bulirsch, R. (2002). *Introduction to Numerical Analysis* (3rd ed.). Springer. https://doi.org/10.1007/978-0-387-21738-3 5. Brotherston, J., & Simpson, A. (2011). “Sequent calculi for induction and infinite descent.” *Journal of Logic and Computation*, 21(6), 1177–1216. https://doi.org/10.1093/logcom/exq052 6. Fowler, M. (2005, December 12). “Event Sourcing.” MartinFowler.com. https://martinfowler.com/eaaDev/EventSourcing.html 7. Chandy, K. M., & Lamport, L. (1985). “Distributed snapshots: Determining global states of distributed systems.” *ACM Transactions on Computer Systems*, 3(1), 63–75. https://doi.org/10.1145/214451.214456 8. Elnozahy, E. N., Alvisi, L., Wang, Y.-M., & Johnson, D. B. (2002). “A survey of rollback-recovery protocols in message-passing systems.” *ACM Computing Surveys*, 34(3), 375–408. https://doi.org/10.1145/568522.568525 9. Dunlap, G. W., King, S. T., Cinar, S., Basrai, M. A., & Chen, P. M. (2002). “ReVirt: Enabling intrusion analysis through virtual-machine logging and replay.” In *Proceedings of the 5th Symposium on Operating Systems Design and Implementation (OSDI ’02)*, 211–224. USENIX Association. https://www.usenix.org/conference/osdi-02/revirt-enabling-intrusion-analysis-through-virtual-machine-logging-and-replay ## Excluded draft references The following draft items are not used as evidence here: - Keller (1968), because the exact edition, publisher record, and intended passage were not confirmed during this check; - Young (2010), because a stable original or author-controlled record was not confirmed; - Brotherston's 2006 thesis, because the journal article above is sufficient for the limited cyclic-proof statement; - adjacent consensus and cryptographic references, because no claim about those fields is needed for this comparison. ### Screening and preservation Screening has three stages: title/snippet, abstract, then accessible full text. For each record retained after title/snippet screening, the log preserves its stable identifier, field, decision, E1–E6 assessment where applicable, and a reason. Searches are reported exactly enough to rerun, with access date and database limitations. One researcher performed the search and screening; no independent duplicate screening or inter-rater agreement is claimed. ### Search strings The fixed rerun submits each family once, with the exact domain restriction and two exact discovery variants preserved in `ANIMUS_CYCLE_PRIOR_ART_SEARCH_LOG.md`. The submitted families are: 1. `("endpoint-derived" OR "terminal-state-derived" OR "final-state-derived") AND (initial OR beginning OR boundary) AND (return OR reconstruction)` 2. `("reciprocal boundary" OR "cyclic boundary condition" OR "periodic boundary condition") AND (execution OR replay OR provenance)` 3. `(fixed point OR self-consistency) AND (checkpoint OR event log OR replay) AND (validation OR provenance)` 4. `("deterministic replay" OR "record and replay") AND (cyclic OR fixed point OR boundary) AND (checkpoint OR reconstruction)` 5. `("event sourcing" OR "event log") AND (cycle OR cyclic OR fixed point) AND (replay OR reconstruction OR validation)` 6. `(workflow OR provenance) AND (cyclic OR loop OR iteration) AND (replay OR reconstruction) AND (validation OR verification)` 7. `(rollback recovery OR distributed snapshot OR checkpoint) AND (fixed point OR self-consistency OR cyclic) AND (endpoint OR boundary)` 8. `(shooting method OR boundary value problem OR periodic solution) AND (replay OR provenance OR event log OR checkpoint)` 9. `(cyclic proof OR circular proof) AND (execution trace OR replay OR provenance OR reconstruction)` The fixed rerun does not claim exhaustive native-database coverage or complete backward/forward citation chasing. Earlier field-oriented searches and citation chasing informed the comparison table, but they are supplementary discovery, not part of the fixed rerun's result counts. This narrower scope is intentional: only searches with complete query and result-level logs contribute to the systematic-search conclusion. ## Included records and equivalence assessment `Y` means the accessible primary source establishes the criterion. `N` is used only when the described method positively uses a different operation, most often no reciprocal endpoint-to-beginning return. `?` means the criterion was not established and is not an inference of absence. | Record | Field | E1 | E2 | E3 | E4 | E5 | E6 | Assessment | |---|---|:---:|:---:|:---:|:---:|:---:|:---:|---| | Crofts, *Efficient Method for Detection of Periodic Orbits in Chaotic Maps and Flows* (2007), [arXiv:0706.1940](https://arxiv.org/abs/0706.1940) | Numerical methods | Y | Y | Y | Y | ? | Y | Strongest reciprocal-closure match. A finite return-map problem is independently checked by interval methods for no or unique solutions, but no provenance-linked replay or reconstruction audit is established. | | Gasull & Mañosa, “Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem” (2018), [arXiv:1809.06208](https://arxiv.org/abs/1809.06208) | Numerical methods | Y | Y | Y | Y | ? | Y | Bounded return-map boxes and independent sign conditions establish existence and number of periodic orbits; provenance and replay are not established. | | Kumar, “A new fast multiple-shooting method for computing periodic orbits...” (2026), [arXiv:2601.00149](https://arxiv.org/abs/2601.00149) | Numerical methods | Y | Y | Y | ? | ? | ? | A finite modulo-\(q\) multiple-shooting system makes the last map return to the first point, but no distinct history validator or provenance/replay audit is established. | | Gander & Wu, “Convergence analysis of a periodic-like waveform relaxation method...” (2019), [doi:10.1007/s00211-019-01060-8](https://doi.org/10.1007/s00211-019-01060-8) | Numerical methods | Y | Y | Y | ? | ? | ? | Endpoint feedback enters the next iterate's initial condition; convergence analysis does not establish the complete validation and audit contract. | | Liu, “When May an Agent Stop? Evidence-Carrying Termination for Tool-Using LLMs” (2026), [arXiv:2608.23623](https://arxiv.org/abs/2608.23623) | Formal verification | Y | N | Y | Y | Y | ? | Strongest auditability match: a trusted contract, immutable evidence, fail-closed validation, and deterministic reconstruction are explicit, but no ending supplies a beginning condition. | | Chang, Geng & Chang, “Mnemosyne: Agentic Transaction Processing for Validating and Repairing AI-generated Workflows” (2026), [arXiv:2607.00269](https://arxiv.org/abs/2607.00269) | Workflow/runtime verification | Y | N | Y | Y | Y | ? | Finite-state constraints, transition logs, deterministic admission, and replay checks are explicit; reciprocal boundary closure is not. | | Nakajima, “The Log is the Agent: Event-Sourced Reactive Graphs for Auditable, Forkable Agentic Systems” (2026), [arXiv:2605.21997](https://arxiv.org/abs/2605.21997) | Event sourcing | ? | N | ? | Y | Y | ? | Append-only lineage, deterministic projection, replay, and strict reproducibility validation are explicit; no endpoint-derived beginning is described. | | Rhodes & Kang, “Proof of Execution: Runtime Verification for Governed AI Agent Actions” (2026), [arXiv:2607.05397](https://arxiv.org/abs/2607.05397) | Runtime verification | ? | N | Y | Y | Y | ? | A fixed execution contract, causal event stream, replay context, and validator are explicit, but the terminal output is not returned as a required beginning condition. | | Geels et al., “Friday: Global Comprehension for Distributed Replay” (2007), [ACM record](https://dl.acm.org/doi/10.5555/1973430.1973451) | Distributed replay | ? | ? | ? | ? | ? | ? | Captures distributed execution, replays it, and checks global predicates. The stricter return-specific provenance and boundary criteria are not established. | | Charapko et al., “Retroscope: Retrospective Monitoring of Distributed Systems” (2019), [doi:10.1109/TPDS.2019.2911944](https://doi.org/10.1109/TPDS.2019.2911944) | Distributed systems | ? | ? | ? | ? | ? | ? | HLC-stamped logs reconstruct consistent global states and test predicates, but no reciprocal boundary contract or separated closure report is established. | | Carbone et al., “Lightweight Asynchronous Snapshots for Distributed Dataflows” (2015), [arXiv:1506.08603](https://arxiv.org/abs/1506.08603) | Distributed systems | ? | ? | ? | ? | ? | ? | Checkpoint and recovery support cyclic dataflows with a minimal log; they do not establish endpoint-derived return and full-history validation. | | O'Callahan et al., “Engineering Record And Replay For Deployability” (2017), [USENIX](https://www.usenix.org/conference/atc17/technical-sessions/presentation/ocallahan) | Deterministic replay | ? | N | ? | ? | ? | ? | Records process inputs and nondeterminism for exact replay; its interface boundary is not a reciprocal temporal boundary. | | Pham, Malik & Foster, “Using Provenance for Repeatability” (2013), [USENIX](https://www.usenix.org/conference/tapp13/technical-sessions/presentation/pham) | Workflow provenance | ? | ? | ? | ? | Y | ? | A provenance trace drives partial deterministic replay in the same event order; no endpoint-to-beginning condition is described. | | Zhuang et al., “ExoFlow: A Universal Workflow System for Exactly-Once DAGs” (2023), [USENIX](https://www.usenix.org/conference/osdi23/presentation/zhuang) | Workflow recovery | ? | N | ? | ? | ? | ? | Durable workflow state coordinates rollback and task replay, but the workflow is a DAG and does not implement reciprocal closure. | | Woodman et al., “Achieving Reproducibility by Combining Provenance with Service and Workflow Versioning” (2011), [doi:10.1145/2110497.2110512](https://doi.org/10.1145/2110497.2110512) | Workflow provenance | ? | N | ? | ? | Y | ? | Complete provenance traces can be transformed into workflows and re-enacted; no ending-derived beginning condition is described. | | Köhler et al., “Improving Workflow Fault Tolerance through Provenance-Based Recovery” (2011), [author-hosted PDF](https://www.cs.ucdavis.edu/~ludaesch/pubs/Improving-Fault-Tolerance-through-Provenance-SSDBM-2011.pdf), [doi:10.1007/978-3-642-22351-8_12](https://doi.org/10.1007/978-3-642-22351-8_12) | Workflow recovery and provenance | ? | N | ? | ? | Y | ? | Uses recorded provenance and checkpoint extensions to resume stateful workflows, including workflow loops, after failure. Its endpoint is a failure/recovery frontier rather than a return that must satisfy an independently frozen beginning contract. | **Screening result:** no record in the assessed set establishes all E1–E6, so no record reached the E7–E9 complete-contract assessment gate. The numerical literature supplies the closest source-supported E1–E4 and E6 combination. Replay, event-sourcing, workflow, and runtime-verification literature supplies the closest E3–E5 combination. The searches did not locate one primary record that joins reciprocal return-map closure to provenance-linked replay/reconstruction and separated outcomes. ## Excluded records retained with reasons | Record or lead | Exclusion reason | |---|---| | Elnozahy et al., “A Survey of Rollback-Recovery Protocols in Message-Passing Systems” (2002), [doi:10.1145/568522.568525](https://doi.org/10.1145/568522.568525) | Secondary survey used for citation chasing, not one candidate method. | | Garg et al., “Deterministic Replay: A Survey” (2015), [doi:10.1145/2790077](https://doi.org/10.1145/2790077) | Secondary survey; no single implementation is assessable for the conjunction. | | “Multiple Shooting Techniques Revisited,” [doi:10.1007/978-1-4684-7324-7_6](https://doi.org/10.1007/978-1-4684-7324-7_6) | Publisher preview confirms boundary-value multiple shooting, but full text was restricted and insufficient for E1–E6. | | Erb et al., “Consistent Retrospective Snapshots in Distributed Event-sourced Systems” (2017) | Relevant lead, but no stable publisher, DOI, repository, or author-controlled full source was verified in this run. | | Tian et al., “Periodic boundary condition and its numerical implementation algorithm...” (2019), [doi:10.1016/j.compositesb.2018.10.053](https://doi.org/10.1016/j.compositesb.2018.10.053) | Ordinary periodic finite-element boundary conditions; no replay/provenance history or endpoint-authored return. | | Jones, “Use of a shooting method to compute eigenvalues of fourth-order ordinary differential equations” (1993), [ScienceDirect](https://www.sciencedirect.com/science/article/pii/037704279390065J) | Standard two-point boundary-value/eigenvalue shooting; no replay, provenance, or history validation. | | Atserias & Lauria, “Circular (Yet Sound) Proofs” (2023), [doi:10.1145/3579997](https://doi.org/10.1145/3579997) | Cyclic proof graph with a soundness condition, not a temporal endpoint-derived return or replayable history. | | Narayanan & Ren, “Circular Trace Reconstruction” (2021), [doi:10.4230/LIPIcs.ITCS.2021.18](https://doi.org/10.4230/LIPIcs.ITCS.2021.18) | “Circular” describes the unknown string; deletion-trace reconstruction does not implement reciprocal executed closure. | | Vidal, “From Reversible Computation to Checkpoint-Based Rollback Recovery...” (2023), [arXiv:2309.04873](https://arxiv.org/abs/2309.04873) | Rollback to an earlier consistent state, without an endpoint-derived beginning return or return-specific validation. | | “RecPlay: A Fully Integrated Practical Record/Replay System,” [doi:10.1145/312203.312214](https://doi.org/10.1145/312203.312214) | “Cyclic debugging” is iterative debugging, not reciprocal temporal closure. | | *Terminal-Universe*, arXiv:2609.04148 | Submitted after the 2026-09-10 cutoff. | ## Systematic-search execution log **Execution date:** 2026-09-12 **Publication cutoff:** 2026-09-10 inclusive **Searchers/screeners:** one primary researcher using five independent field-focused search passes; final decisions consolidated under the frozen criteria above. All nine frozen query families were rerun once in a fixed domain matrix. The matrix returned 72 rows representing 64 canonical unique records. Every row, exact query, domain restriction, result count, duplicate, and title/snippet decision is preserved in `ANIMUS_CYCLE_PRIOR_ART_SEARCH_LOG.md`. | Pass | Query families and principal variants | Indexes or stable-source surfaces reached | |---|---|---| | Formal methods | F1, F3, F4, F6, F7, F9; fixed-point certificates, model checking, cyclic proofs, runtime verification, provenance | ACM DL, IEEE Xplore, arXiv, USENIX, DROPS, author-controlled proceedings copies | | Distributed systems and replay | F3–F7 plus distributed replay, consistent cuts, replicated logs, global predicates, event-sourced snapshots | ACM DL, IEEE Xplore, dblp, USENIX, arXiv, SpringerLink, ScienceDirect | | Numerical boundary methods | F1–F4 and F8; periodic orbits, return maps, multiple shooting, interval validation, waveform relaxation | arXiv, SpringerLink, SIAM, ScienceDirect, IEEE Xplore, Crossref | | Workflow and provenance | F1–F9; cyclic workflows, process mining, provenance replay, fault recovery, event logs | ACM DL, IEEE Xplore, USENIX, dblp, SpringerLink, ScienceDirect, Crossref, OpenAlex, Semantic Scholar, PMC | | Cross-domain conjunction | F1–F9 plus six targeted combinations joining return maps, endpoint feedback, deterministic replay, provenance, validation, and multiplicity | ACM DL, IEEE Xplore, arXiv, USENIX, SpringerLink, ScienceDirect, OpenAlex, Semantic Scholar, Oxford Academic | Earlier field-oriented discovery and citation chasing used these additional strings: - `"self-consistent" initial conditions replay provenance validation finite`; - `"closed-loop" workflow provenance replay validation endpoint`; - `"periodic orbit" shooting method continuation replay reconstruction uniqueness`; - `"fixed point" "event log" deterministic replay provenance`; - `"return map" endpoint initial condition provenance replay`; and - `"replay" "multiple solutions" boundary value provenance`. The fixed rerun was deduplicated by DOI, arXiv identifier, or canonical URL. Positive E assessments require accessible primary text. Abstract-only, paywalled, and insufficient records are retained as exclusions or unresolved leads rather than treated as negative evidence. **Follow-up retrieval, 2026-09-18:** An author-hosted primary PDF was located for Köhler et al., “Improving Workflow Fault Tolerance through Provenance-Based Recovery.” The record was moved from the unresolved-lead table to the included equivalence assessment. It strengthens the workflow provenance/replay comparison but does not satisfy E2 because recovery resumes a failed workflow from provenance or checkpoints rather than deriving a return from an executed endpoint that must satisfy an independently frozen beginning contract. ### Sources and coverage The search covers records dated from database inception through 2026-09-10. The fixed rerun targets these public index and publisher surfaces: - ACM Digital Library and IEEE Xplore for distributed systems, replay, checkpointing, workflow, and formal methods; - USENIX proceedings for systems and replay; - arXiv for openly indexed computer science and numerical work; - SpringerLink and ScienceDirect for numerical methods, boundary-value problems, workflow, and provenance literature; and - Oxford Academic for formal-method discovery. Earlier supplementary discovery reached dblp, Crossref, Semantic Scholar, and OpenAlex, but those searches are not included in the fixed rerun's counts or systematic-search conclusion because their result-level logs were not retained. Search-engine results may locate a record, but inclusion requires a stable publisher, proceedings, repository, DOI, or author-controlled source. ### Eligibility criteria A record is included for full-text equivalence assessment when it: 1. was publicly available by 2026-09-10; 2. describes a technical method, formal model, or implemented system; 3. concerns at least two elements of the conjunction: reciprocal boundary closure, executed endpoint derivation, replay/reconstruction, independently declared validation, or explicit provenance; and 4. has enough accessible primary text to assess what the method requires. Records are excluded from equivalence assessment when they are duplicate versions, secondary summaries without additional technical content, use “cycle” only as a scheduling or iteration label, concern only ordinary periodic boundary conditions, or lack accessible text sufficient to test the criteria. Every returned row, including irrelevant keyword hits, is retained in the execution log with a reason. ### Preliminary equivalence screen and complete-contract rule E1–E6 are necessary preliminary criteria for identifying the nearest cross-disciplinary matches: - **E1 finite declared evaluation domain:** a finite state, trace, candidate, or bounded execution domain is declared for the result; - **E2 reciprocal executed boundary:** forward execution from a candidate beginning reaches an ending, and content derived from that executed ending supplies a condition required at the beginning; - **E3 result-independent beginning contract:** the beginning or boundary acceptance conditions are declared independently of the observed candidate result; - **E4 independent validation:** a distinct check evaluates the sealed or completed history against beginning, endpoint, and return requirements; - **E5 provenance and replay/reconstruction:** the method records the origin of the return and supports deterministic replay or a declared reconstruction rule sufficient to audit it; - **E6 separated outcomes:** closure/existence is reported separately from at least uniqueness or multiplicity, replay, information retention/loss, or state equality. A **complete contract match** must satisfy E1–E6 and also: - **E7 causal ablation:** removing the returned beginning fact prevents the validated returned content from being derived; - **E8 bounded observers:** observer output is explicitly local and excludes the hidden global state, boundary, contract, return, enumeration, and validation metadata; and - **E9 one authoritative history:** candidate search is a validation procedure, not represented branching, except under an explicitly declared branch intervention. These nine criteria map the required invariants in `ANIMUS_CYCLE.md`: E1 maps the finite domain; E2 maps forward execution and ending-derived return; E3 maps the beginning contract; E4 maps independent sealed-history validation; E5 maps return provenance, replay, and reconstruction; E6 maps separated outcomes; and E7–E9 map causal ablation, bounded observers, and one authoritative history. Functional equivalence counts even when terminology differs. A record that fails or leaves any E criterion unclear is a partial match, not a complete match. Because no assessed record passed E1–E6, none reached the E7–E9 full-contract assessment gate. ## Systematic-search conclusion This search **did not identify a complete E1–E9 match**. No record passed the E1–E6 preliminary gate, so none could qualify for the complete-contract E7–E9 assessment. The search therefore improves the comparison from an unsystematic source check to a documented negative search result. It does **not** establish a true prior-art gap. Non-retrieval cannot prove absence, several promising records were inaccessible, database searches were mediated by public web indexes rather than authenticated native database APIs, terminology may differ, citation chasing was bounded, and screening was performed by one researcher. The supported conclusion is: > Across the documented searches and accessible primary records through > 2026-09-10, we identified close partial precedents but no source-supported > record satisfying the frozen complete-contract criteria. This is a > documented negative search result, not proof that the conjunction is absent > from prior systems and not a scientific or technical novelty claim. Before any novelty language is considered, the remaining inaccessible leads should be obtained, and qualified external reviewers should independently rerun or challenge the search and equivalence decisions. ### Research question Does a record published before 2026-09-11 describe a single finite-system method or implementation that satisfies the complete Animus-cycle conjunction, rather than merely one or more neighboring mechanisms? OSF Registration metadata Title The Animus Cycle: A Design Specification for Reciprocal-Boundary Closure in Finite Systems Authors and accountable contributors 1. Cholee Hackett, first author 2. Kelly Hackett, co-author and research sponsor Kelly Hackett provided financial and non-financial sponsorship for this research. Both authors must be added as OSF contributors and approve the Registration. Record status Registration of an existing proposed design specification using the Open-Ended Registration template. This is not a prospective preregistration, completed experiment, or Test 05 result. Short description The Animus cycle is a proposed reciprocal-boundary closure pattern for finite systems. The term "Animus cycle" is used here in the proposed technical sense introduced by Hackett & Hackett (2026): a finite-system run whose ending produces and validates a return that satisfies the run's beginning contract under a declared reconstruction rule. Forward execution from the candidate beginning must produce the ending from which that return is independently derived. Thus closure is reciprocal: the beginning produces the ending, and the ending supplies a condition required by the beginning. Information loss is not required for closure, and any continuity through information loss is optional and reported separately. The specification defines eight named validation predicates, bounded-observer exclusions, retention roles, NONE, UNIQUE, and MULTIPLE history classifications, and a default prohibition on branching unless ORIGIN_CUT is declared in advance. The stronger optional Animus Omega Cycle, technically the Animus Omega branch-reconvergence cycle, begins with one authoritative history, permits declared represented branches during expansion, and reconciles them under a frozen narrative-equivalence rule during contraction until one canonical history remains. Branch reconvergence, information loss, continuity through loss, and reciprocal closure are reported separately. A built-in deterministic browser trace illustrates the sequence but is not Test 05 evidence. Any future reserved branch-reconvergence experiment requires a separate, prospectively time-locked protocol with matched controls and independently scored outcomes. Frozen reference fixtures provide a passing example, an endpoint-mutation failure, and a separately versioned declared ORIGIN_CUT example. They are executable teaching examples, not Test 05 evidence. Tests 01-04 are separate retrospective measurements of adjacent components and do not establish the complete Animus cycle. Keywords Animus cycle; Animus Omega; Animus Omega Cycle; Animus Omega branch-reconvergence cycle; reciprocal-boundary closure; finite systems; beginning contract; ending-derived return; sealed-history validation; deterministic replay; bounded observer; state reconstruction; event sourcing; checkpointing; fixed-point constraints; reproducible specification Language English Licensing The author-written specification, claims boundary, fixture documentation, and Registration narrative are licensed under Creative Commons Attribution 4.0 International. The simulator source is Copyright 2026 Hackett & Hackett: Cholee Hackett and Kelly Hackett. All rights reserved. Public availability permits inspection but does not grant a general license to modify, redistribute, or reuse the source. Identifier warning Do not add a DOI, OSF identifier, URL, deposit date, or publication status until OSF assigns it. # The Animus Omega Conjecture ## Cyclic Boundary Dependence and Narrative Continuity in Finite Simulations **Cholee Hackett** Independent researcher September 11, 2026 Preprint version 1.1 **Version 1.1 clarification:** Cyclic closure does not require information loss. Continuity through optional information loss is a separate, stronger hypothesis. This clarification changes no completed Test 01–04 evidence and reports no Test 05 result. ## Abstract The Animus Omega conjecture proposes that a finite persistent simulation could organize its history as a cyclic process of expansion, contraction, and return. The ending of a complete history supplies conditions used to construct the next beginning, while forward execution from that beginning produces the ending. The two boundaries are therefore mutually constrained rather than independent. Histories are globally constrained because only trajectories compatible with both boundary conditions qualify as closing histories. As a separate optional extension, the conjecture asks whether a protected narrative ledger could preserve high-level continuity across a lossy boundary. The ledger would retain stable identities, relationships, obligations, unresolved causes, and other task-relevant invariants while lower-level microstate is discarded or reconstructed. Information loss is not required for cyclic closure. For specified bounded observers, a successful implementation would use a frozen decision procedure that finds no qualifying distinction between boundary-crossing and matched interior observations. This paper states the conjecture as a bounded software research program. It does not claim that the physical universe is simulated or cyclic, that consciousness survives a reset, that inhabitants are subjectively unaware, or that the proposed architecture is computationally superior to established methods. Tests 01 through 04 provide separate methodological foundations but do not validate reciprocal cyclic closure. A proposed Test 05 would evaluate closure independently from optional information loss, narrative obligation preservation, bounded-observer behavior, and resource performance in one deterministic finite model. ## 1. Status and scope This document is a theoretical preprint. It introduces a conjecture and a program for testing it. It is not a preregistration, a retrospective registration, a report of Test 05 results, or evidence that the complete architecture works. The scientific scope is deliberately narrow. The proposed tests concern finite software objects with explicit states, transitions, observers, ledgers, and resource measurements. Results from such objects may establish mathematical or engineering properties within the tested domain. They cannot by themselves establish claims about physical cosmology, consciousness, subjective identity, free will, or the ontological status of our universe. ## 2. Originating conjecture The stronger Animus Omega conjecture contains the following claims as proposed properties of a finite simulation: 1. The simulation may use a periodic spatial topology. 2. Independently of spatial topology, its complete history may satisfy a temporal closure condition. 3. Its represented world expands, reaches a defined limit, contracts, and begins again. 4. The transition from ending to beginning is causally coherent. 5. The ending creates or carries conditions required by the beginning. 6. Forward execution from the beginning eventually creates that ending. 7. Beginning and ending are mutually constrained because each participates in the conditions that make the other possible. 8. Complete histories must satisfy both independently specified beginning requirements and ending-derived return requirements. 9. Only histories consistent with the full cycle qualify as closing histories. 10. A frozen decision procedure may find no qualifying distinction between boundary and interior observations for specified inhabitants or observers using their permitted observations, retained memory, relationships, and causal obligations. 11. The architecture may preserve high-level fidelity while discarding or reconstructing lower-level state. These statements form one conjecture, but they are not one indivisible hypothesis. Each must be operationalized and adjudicated separately. ## 3. Spatial torus, temporal closure, and recurrence A spatial torus joins opposite spatial boundaries. An inhabitant crossing one edge reappears through the corresponding opposite edge without encountering a spatial wall. This topology alone does not imply temporal recurrence, expansion, contraction, or an ending that creates a beginning. Temporal closure requires a different condition. Let a finite state be \(S_t\) and let deterministic or explicitly stochastic transition dynamics be \(F\). A conventional period-\(T\) recurrent trajectory satisfies: \[ F^T(S_0) = S_0 \] for some period \(T\). Recurrence alone is still weaker than reciprocal boundary dependence. A replayed loop can return to its initial bytes without its ending causally helping construct its next beginning. Information loss, narrative obligations, and bounded observers are separate properties rather than requirements for cyclic operation. The stronger proposal uses a period-\(T\) history with \(T-1\) ordinary forward transitions and one executed boundary transition. In the proposed twelve-tick world, ordinary forward execution produces states \(S_0\) through \(S_{11}\), and the boundary transition constructs \(S_{12}\). The formal model separates these objects: \[ B_0 = B(S_0) \] where \(B_0\) is a locked projection of beginning requirements fixed before endpoint execution; \[ (S_0,\ldots,S_{T-1}) = F(S_0, A_{0:T-2}) \] where forward dynamics produce the endpoint; \[ E_{T-1} = R(S_{T-1}) \] where \(E_{T-1}\) is the endpoint-derived return value; and: \[ Q_{T-1} = K(S_{T-1}) \] where \(Q_{T-1}\) is the boundary payload. In a lossless arm, \(K\) may preserve a complete checkpoint. In an optional lossy arm, \(K(S_{T-1})=G(D(S_{T-1}))\), where \(D\) creates a genuinely lossy residual and \(G\) produces a reconstructed payload; and: \[ S_T = J(E_{T-1}, L_{T-1}, Q_{T-1}, C) \] where \(J\) is the executed boundary transition, \(L_{T-1}\) is the protected ledger at the endpoint, and \(C\) contains only locked rules and fixed external conditions. Two closure levels must be reported separately: 1. **Requirement-level closure:** \(E_{T-1} = B_0\). 2. **Executed state closure:** the actual boundary transition constructs \(S_T\), after which the locked beginning projection satisfies \(B(S_T) = B_0\). Exact recurrence is a stronger optional condition, \(S_T = S_0\), and must not be inferred from requirement-level closure. The endpoint-derived value must participate in constructing or validating the next state. The initial requirements must be fixed independently before the endpoint is computed. Defining the beginning by applying \(R\) to a chosen ending and then calling the result closure would be circular. Until an ending-derived value participates in an executed boundary transition, the system demonstrates endpoint compatibility rather than an ending that creates its beginning. ## 4. The ending and beginning handshake The phrase "the ending and beginning shake hands" refers to reciprocal boundary dependence. The beginning contributes: - initial identities and relations; - available resources; - unresolved obligations; - permitted actions; - conditions from which the future history develops. The ending contributes: - a return token or reconstructive condition; - fulfilled and unresolved obligations; - stable relation requirements; - retained causal information; - constraints required for the next beginning to be valid. The proposal is not merely that the ending resembles the beginning. It is that the ending carries information used by the executed boundary transition to construct or validate the next beginning, while the beginning generates the history that produces that ending. This dependence must be tested by intervention. If the endpoint token, intermediate action, protected obligation, or required relation is changed, a valid test should detect that the history no longer closes. A structure that closes under every perturbation does not demonstrate meaningful boundary dependence. ## 5. Globally constrained histories The intuitive term "predestined narrative" is translated into a narrower computational statement: > A complete finite history is globally constrained when independently fixed > beginning requirements and ending-derived return requirements admit only a > defined subset of possible histories. This definition does not claim that human lives are predetermined. It does not resolve philosophical disputes about free will. It describes a property of a finite transition system. Suppose a world permits multiple local actions during its expansion phase. The action domain may contain closing and non-closing trajectories. A globally constrained history is one that satisfies the forward rules and the boundary requirements simultaneously. The strength of the constraint can be measured by: - the number of admissible action histories; - the number and proportion of closing histories; - whether closing histories form one primitive cycle or several; - whether endpoint or intermediate interventions destroy closure; - whether non-closing alternatives remain genuinely reachable. If only one action is ever possible, closure may be a scripted artifact. A credible model therefore requires multiple reachable choices and both closing and non-closing histories. ## 6. Proposed simulator architecture ### 6.1 Authoritative trunk One canonical state controls the world clock, entity identities, relations, resources, obligations, and accepted events. Observer threads do not write directly to this state. ### 6.2 Observer or region threads Observers receive bounded local views and working memory. Their observations must omit hidden global state, absolute phase labels, and any explicit return marker unless a control arm grants that information. ### 6.3 Protected narrative ledger The protected ledger records high-level information that must remain coherent: - stable identities; - directed and undirected relationships; - permissions and ownership; - promises and obligations; - dependencies between obligations; - deadlines and fulfillment; - unresolved causes; - provenance linking state changes to accepted events. The ledger is not proof of consciousness or personal identity. It is an engineering representation of declared continuity requirements. ### 6.4 Expansion During expansion, the world permits multiple local viewpoints, actions, and microstates. Represented detail and observer-specific state may grow within a fixed resource envelope. ### 6.5 Contraction and optional dump Contraction does not by itself require information loss. A lossless arm may retain a complete state or checkpoint. In an optional lossy arm, selected microstate is unloaded, summarized, or discarded. That arm's information-loss function must be explicit and non-injective: at least two admissible prior microstates must map to the same retained residual. ### 6.6 Deterministic merge Observer or region proposals are merged under an explicit conflict rule. Accepted events update the authoritative trunk in canonical order. Duplicate, orphaned, contradictory, and stale writes must be detectable. ### 6.7 Reconstruction and return The executed boundary transition combines a boundary payload with the endpoint-derived return value, protected ledger, and locked conditions to construct the next beginning state. A lossless arm may obtain that payload from a complete checkpoint. In an optional lossy arm, the dump function maps the endpoint to a lossy residual and the reconstruction function maps that residual to a reconstructed payload. The endpoint-derived value is compared with independently fixed beginning requirements, and the constructed state's beginning projection is checked against those requirements. ## 7. Optional continuity through information loss This section applies to the optional lossy-continuity hypothesis, not to cyclic closure generally. High-level fidelity cannot mean only "the reconstruction retains whatever was chosen for retention." That would make success tautological. Before execution, a test must identify independently meaningful fields, behaviors, and consequences, such as: - stable identity; - relationship consistency; - obligation fulfillment; - causal dependency order; - access permissions; - resource ownership; - observer-visible consequences; - task completion. Let \(H(S_T)\) be the locked high-level semantic projection of the constructed post-boundary state. Let \(H^*(S_0,\ldots,S_{T-1},B_0)\) be a semantic target fixed by the protocol before confirmatory execution and calculated from independently meaningful history and boundary requirements. A minimal exact-fidelity condition is: \[ H(S_T) = H^*(S_0,\ldots,S_{T-1},B_0) \] This equality must be evaluated while also showing that \(Q_{T-1}=G(D(S_{T-1}))\) contributes to constructing \(S_T\) and that \(D\) discards information. If \(D\) retains every field required to reconstruct the complete endpoint, the test is ordinary lossless checkpointing rather than lossy continuity. Every semantic field must be classified before execution as: - copied directly into the retained ledger or residual; - reconstructed from retained information; - derived by executing post-boundary dynamics; - intentionally discarded. Directly copied ledger fields demonstrate preservation, not reconstruction. The main fidelity test must also evaluate locked downstream behaviors and observer-visible consequences that are not satisfied merely by copying their expected answers into the ledger. Baseline arms must receive the same continuity obligations and must be scored by the same semantic projection. ## 8. Observer boundary indistinguishability The phrase "inhabitants remain unaware" cannot be tested as subjective experience. It is operationalized as a bounded observation claim: > Under a frozen test, a specified decision procedure finds no distinction > meeting its locked criterion between boundary-crossing and matched interior > observation windows for a stated observer class and sampling distribution. Let \(O_i\) be the observation function for observer \(i\). Boundary and interior windows must have equal width and matched phase-relevant conditions. They must exclude absolute tick, hidden global state, and explicit reset labels. Possible measures include: - exact equality of observation-sequence distributions; - total variation distance; - a frozen bounded classifier; - a label-permutation baseline; - per-observer detection rates. The protocol must freeze the window width, sampling process, phase matching, null model, statistic, threshold, uncertainty calculation or exact-enumeration rule, and positive-control acceptance criterion before confirmatory execution. If exact equality is established by exhaustive enumeration, that stronger fact may be reported directly. Otherwise, failure to cross a detection threshold must not be described as proof that observers cannot distinguish the boundary. A full-view observer should serve as a positive control. If no observer, including one given global state and boundary markers, can detect the boundary, the detection test may be defective. Any conclusion applies only to the specified observer class and tested distribution. It does not establish that every possible observer would remain unaware. ## 9. Computational and resource claim The architecture may reduce retained state, but a storage reduction alone is not a computational advantage. Reconstruction, synchronization, and fidelity failures may cost more than the state that was removed. A complete comparison should report: - peak live bytes across the authoritative trunk, ledger, observer buffers, residuals, event logs, checkpoints, and temporary reconstruction state; - cumulative byte-ticks across all arm-specific live storage; - checkpoint or residual size; - deterministic operation count; - dump and reconstruction work; - synchronization and conflict-resolution work; - observer update and observation-generation work; - wall-clock time; - semantic mismatch count; - observer-visible mismatch count; - obligation failures. The primary arm should be compared with: - uninterrupted execution; - ordinary complete checkpoints; - always-expanded lossless execution; - snapshots plus event logs; - an open chain with no return; - no-loss and no-ledger ablations; - a scripted repeating loop; - a compute-matched random ending. Support for a resource hypothesis requires the closure and fidelity gates to pass first. Comparisons must use matched horizons, action histories, semantic obligations, observer-output obligations, and measurement scope wherever the arm permits. Wall time requires a frozen repeated-run method and separate reporting of warmup, number of repetitions, and variation. Support requires a named matched baseline to be beaten on prespecified total-cost criteria, not only checkpoint or residual size. Any supported result would remain limited to the tested finite model. ## 10. Relationship to Tests 01 through 04 ### Test 01: reset-persistence measurement Test 01 validated a method and calibrated a future threshold for measuring selected joint-state dependence after a lossy transformation. It provides measurement ideas for Test 05 but no independent confirmatory coupling effect. ### Test 02: exact bounded primitive closure Test 02 exhaustively enumerated all 66,064 labeled binary relations for state sizes 2, 3, and 4 at periods 1 through 8. It establishes exact bounded facts about primitive cycles. It does not establish an inhabited narrative, causal boundary dependence, or general uniqueness. ### Test 03: carried-state prediction Test 03 asked whether carried recurrent state improved a locked prediction endpoint against an approximately parameter-matched fixed-window model. The criterion failed: \(Q<0\) occurred in 0 of 20 reserved-seed bundles and mean \(Q=0.6826707925423762\). This unsupported result is important negative evidence against assuming that recurrence automatically provides a computational advantage. ### Test 04: exact checkpoint replay Test 04 Revision 1 was operationally aborted and supplies no result. Revision 2 passed all 60 prespecified replay arms under its frozen protocol, with exact immediate restoration and no future semantic-state or observer-output mismatches through tick 4096. Test 04 establishes exact complete-checkpoint replay in one deterministic implementation. It does not establish lossy reconstruction, narrative closure, resource savings, or subjective continuity. ### Foundation, not proof Tests 01 through 04 provide measurement, exact enumeration, negative resource-prediction evidence, replay methods, and evidence-preservation discipline. They do not combine into evidence for the complete Animus Omega conjecture. ## 11. Proposed Test 05 Test 05 is intended to evaluate the conjecture's parts independently in one small deterministic world. Its development plan specifies: - three stable identities; - a four-cell ring; - two bounded radius-one observers; - two directed relationships; - two causally chained obligations; - one contested resource; - a twelve-tick history; - expansion during ticks 3 through 7; - contraction during ticks 8 through 10; - a return boundary at tick 12; - an exhaustive finite action domain containing closing and non-closing histories. The four-cell ring instantiates one spatial topology, and the tick schedule instantiates one expansion and contraction pattern. Without matched non-ring topology arms and alternative phase schedules, Test 05 cannot establish that a ring, expansion, or contraction is necessary or advantageous. Test 05 separates six hypotheses: 1. engineering feasibility; 2. exact reciprocal closure; 3. genuine information loss with bounded semantic fidelity; 4. specified-observer boundary indistinguishability; 5. protected narrative obligation preservation; 6. bounded resource performance against matched baselines. The study remains in development. No valid Test 05 result is reported in this paper. Development output must not be retained as evidence until a documented technical audit confirms that outcomes are calculated from executed arms rather than hard-coded labels or circular definitions. The current design review used an AI architect tool and is not independent peer review. ## 12. Falsification conditions Each Test 05 hypothesis can fail independently in the tested model. Failure of the optional information-loss hypothesis does not by itself refute reciprocal cyclic closure. Examples of component failures include: - no history satisfies independently fixed beginning and ending conditions; - every reachable history closes, making the boundary constraint non-discriminating; - endpoint or intermediate interventions do not break closure; - an arm designated as lossy uses an injective dump and is therefore not genuinely lossy; - high-level obligations fail after reconstruction; - local observers reliably detect the boundary; - the full-view positive control cannot detect the boundary; - resource savings disappear after reconstruction and synchronization costs are counted; - simpler checkpointing or event-sourcing baselines achieve equal fidelity at lower total cost; - results depend on iteration order, undocumented state, or outcome-based exclusions. A mixed result is expected to remain possible. For example, reciprocal closure could succeed in a lossless arm while continuity through loss or the resource comparison fails. Each hypothesis must be reported independently. A separate combined lossy-closure status may be reported, but it must not replace the standalone closure result. ## 13. Alternative explanations and controls A successful result could still have simpler explanations: - a hard-coded loop; - a complete hidden checkpoint; - an observer too weak to detect anything; - a fidelity definition that ignores every discarded field; - an endpoint selected after inspecting outcomes; - a ledger that records obligations but does not affect dynamics; - unmatched resource baselines; - a classifier or threshold selected after seeing confirmatory labels. Required controls must therefore include malformed return data, endpoint interventions, intermediate action changes, ledger deletion, identity shuffling, stale and duplicate events, no-loss execution, full-view observers, ordinary complete checkpoints, and compute-matched non-closing endings. ## 14. Interpretation boundaries Even a fully supported Test 05 would justify only bounded statements such as: - the architecture can be implemented in the tested deterministic model; - an executed ending can satisfy defined conditions required by an independently fixed beginning; - selected high-level invariants can survive a declared lossy transformation; - specified observers did not distinguish the boundary under a frozen test; - the tested implementation had measured costs relative to named baselines. It would not establish: - that the physical universe is a simulation; - that physical time is cyclic; - that consciousness or subjective identity survives a reset; - that inhabitants in general would remain unaware; - that individual lives are predetermined; - that the architecture is generally more efficient; - that Animus Omega is technically novel. Novelty and priority require a comparative literature review. Safety-critical, medical, financial, governmental, transportation, and infrastructure applications require separate domain validation and regulatory analysis. ## 15. Related technical domains Animus Omega combines questions that are already studied separately in distributed systems, checkpointing, event ordering, constraint satisfaction, and time-symmetric boundary models. Similarity to those domains does not establish equivalence or novelty. Distributed snapshot and event-ordering research provides methods for defining consistent states and causal order in systems with multiple processes [1, 2]. Data-system design literature describes logs, state derivation, replication, and recovery patterns relevant to the proposed trunk and ledger [3]. Constraint-processing research provides a general framework for histories restricted by simultaneous conditions [4]. Time-symmetric formulations in physics illustrate the mathematical use of initial and final boundary conditions, but they do not validate the proposed software architecture or any cosmological interpretation [5]. A complete novelty review remains future work. The present paper claims only a specific conjecture and test program. ## 16. Open research questions 1. What is the smallest nontrivial world in which reciprocal closure cannot be reduced to a scripted loop? 2. Which semantic fields are independently meaningful enough to define high-level fidelity? 3. How much information can be removed before obligations or observer-visible consequences fail? 4. Can observer-boundary indistinguishability survive stronger observer classes? 5. Can mutually constrained boundaries coexist with multiple reachable local choices? 6. Does globally constrained closure improve any engineering outcome relative to standard checkpoints, event logs, or state-machine replication? 7. How should reconstruction and synchronization costs be included in total resource accounting? 8. Under what conditions do multiple closing histories exist, and how should one be selected without outcome-dependent bias? ## 17. Evidence and provenance The completed Tests 01 through 04 are preserved separately in the immutable public evidence bundle: `exact-evidence-tests-01-04-2026-09-10.zip` The bundle has its own checksum, manifests, reports, source archives, correction notices, and verification instructions. This preprint does not modify or replace that frozen evidence. No OSF identifier, DOI, or theory-preprint URL is asserted in this version. Add those values only after the relevant service assigns them. ## 18. Funding, interests, and attribution Tests 01 through 04 received no external funding. This theoretical preprint also received no external funding. The author is co-founder of BatchBuddy, a commercial compliance platform, and serves as president of The Love Tower at Ashah, a separate nonprofit. Neither organization funded this work, and neither organization is part of the evidence record. Cholee Hackett is the sole author and accountable contributor. AI systems were used as tools for drafting, code assistance, criticism, and document preparation. They are not authors or independent replicators. ## 19. License Copyright 2026 Cholee Hackett. This author-written theoretical preprint is licensed under the Creative Commons Attribution 4.0 International license. Software, data, binaries, and third-party material retain their own licenses or notices. This narrative license does not automatically relicense them. ## 20. Companion records - *Persistence and Primitive Closure in Finite Computational Systems*: the retrospective Tests 01 through 04 evidence record. - *Test 05 development plan: bounded narrative closure*: the current AI-assisted technically audited design for the combined simulator study. - Future Test 05 prospective registration: to be created only after the implementation, arm matrix, metrics, thresholds, failure rules, and reserved seeds are frozen and time-locked. ## References 1. Chandy, K. M., and Lamport, L. (1985). Distributed snapshots: Determining global states of distributed systems. *ACM Transactions on Computer Systems*, 3(1), 63–75. https://doi.org/10.1145/214451.214456 2. Lamport, L. (1978). Time, clocks, and the ordering of events in a distributed system. *Communications of the ACM*, 21(7), 558–565. https://doi.org/10.1145/359545.359563 3. Kleppmann, M. (2017). *Designing Data-Intensive Applications*. O'Reilly Media. 4. Dechter, R. (2003). *Constraint Processing*. Morgan Kaufmann. 5. Aharonov, Y., Bergmann, P. G., and Lebowitz, J. L. (1964). Time symmetry in the quantum process of measurement. *Physical Review*, 134(6B), B1410–B1416. https://doi.org/10.1103/PhysRev.134.B1410 # The Animus Omega Conjecture ## Cyclic Boundary Dependence and Narrative Continuity in Finite Simulations **Cholee Hackett** Independent researcher September 11, 2026 Preprint version 1.2 **Version 1.2 addition:** This version defines the canonical term *Animus cycle*, records the relationship between that contract and the wider Animus Omega research program, states the associated claims boundary, and defines an optional stronger version named the *Animus Omega Cycle*, technically the *Animus Omega branch-reconvergence cycle*. Information loss remains optional and continuity through loss remains a separate, stronger hypothesis. A built-in deterministic browser trace now illustrates the branch-reconvergence sequence without serving as evidence. A future reserved experiment requires a separate, prospectively time-locked protocol. This addition changes no completed Test 01–04 evidence and reports no Test 05 result. ## Abstract The Animus Omega conjecture proposes that a finite persistent simulation could organize its history as a cyclic process of expansion, contraction, and return. The ending of a complete history supplies conditions used to construct the next beginning, while forward execution from that beginning produces the ending. The two boundaries are therefore mutually constrained rather than independent. Histories are globally constrained because only trajectories compatible with both boundary conditions qualify as closing histories. The **Animus Omega Cycle** is the public name for the stronger branch-reconvergence version. Technically, this **Animus Omega branch-reconvergence cycle** begins with one authoritative history, permits declared represented branches during expansion, and reconciles them in stages during contraction under a frozen narrative-equivalence rule. Reconvergence must leave one authoritative history before return. The Animus Omega Cycle is not required by the minimum Animus-cycle definition, and it is separate from candidate-history enumeration. As a separate optional extension, the conjecture asks whether a protected narrative ledger could preserve high-level continuity across a lossy boundary. The ledger would retain stable identities, relationships, obligations, unresolved causes, and other task-relevant invariants while lower-level microstate is discarded or reconstructed. Information loss is not required for cyclic closure. For specified bounded observers, a successful implementation would use a frozen decision procedure that finds no qualifying distinction between boundary-crossing and matched interior observations. This paper states the conjecture as a bounded software research program. It does not claim that the physical universe is simulated or cyclic, that consciousness survives a reset, that inhabitants are subjectively unaware, or that the proposed architecture is computationally superior to established methods. Tests 01 through 04 provide separate methodological foundations but do not validate reciprocal cyclic closure. A proposed Test 05 would evaluate closure independently from optional information loss, narrative obligation preservation, bounded-observer behavior, and resource performance in one deterministic finite model. ## 1. Status and scope This document is a theoretical preprint. It introduces a conjecture and a program for testing it. It is not a preregistration, a retrospective registration, a report of Test 05 results, or evidence that the complete architecture works. The scientific scope is deliberately narrow. The proposed tests concern finite software objects with explicit states, transitions, observers, ledgers, and resource measurements. Results from such objects may establish mathematical or engineering properties within the tested domain. They cannot by themselves establish claims about physical cosmology, consciousness, subjective identity, free will, or the ontological status of our universe. ## 2. The Animus cycle An **Animus cycle (Hackett, 2026)** is a finite-system run whose ending produces and validates a return that satisfies the run's beginning contract under a declared reconstruction rule. Forward execution from the candidate beginning must produce the ending from which that return is independently derived. A successful cycle therefore requires reciprocal closure: the beginning produces the ending, and the ending supplies a condition required by the beginning. This paper uses the following relationship map: - **Animus Omega** is the research program. - **An Animus cycle** is the reciprocal-boundary closure contract defined here. - **Tests 01–04** are separate retrospective measurements of adjacent components. - **The conceptual simulator** is an executable teaching model. - **Test 05** is the proposed controlled test of the combined cycle contract. Information loss is not part of the definition. Exact recurrence, complete checkpoint return, lossless reconstruction, and lossy reconstruction are different candidate architectures. Continuity through information loss is an optional, stronger hypothesis and must be tested and reported separately from closure. A protected ledger alone is not evidence of continuity through loss. The proposed contribution is this named contract and its separated validation outcomes, not priority over checkpointing, event sourcing, deterministic replay, fixed-point or self-consistency constraints, bounded-observer models, or state reconstruction. The definition does not establish legal exclusivity, scientific novelty, physical recurrence, consciousness, subjective continuity, cosmology, unrestricted predestination, or a general computational advantage. ## 3. Originating conjecture The stronger Animus Omega conjecture contains the following claims as proposed properties of a finite simulation: 1. The simulation may use a periodic spatial topology. 2. Independently of spatial topology, its complete history may satisfy a temporal closure condition. 3. Its represented world expands, reaches a defined limit, contracts, and begins again. 4. The transition from ending to beginning is causally coherent. 5. The executed ending derives or carries data that participates in reconstructing conditions required by the beginning. 6. Forward execution from the beginning eventually creates that ending. 7. Beginning and ending are mutually constrained because each participates in the conditions that make the other possible. 8. Complete histories must satisfy both independently specified beginning requirements and ending-derived return requirements. 9. Only histories consistent with the full cycle qualify as closing histories. 10. A frozen decision procedure may find no qualifying distinction between boundary and interior observations for specified inhabitants or observers using their permitted observations, retained memory, relationships, and causal obligations. 11. The architecture may preserve high-level fidelity while discarding or reconstructing lower-level state. 12. In a stronger optional architecture, one authoritative history may create declared represented branches during expansion and reconcile them during contraction until one beginning-compatible history remains. These statements form one conjecture, but they are not one indivisible hypothesis. Each must be operationalized and adjudicated separately. ## 4. Spatial torus, temporal closure, and recurrence A spatial torus joins opposite spatial boundaries. An inhabitant crossing one edge reappears through the corresponding opposite edge without encountering a spatial wall. This topology alone does not imply temporal recurrence, expansion, contraction, branch creation, branch reconvergence, or an endpoint whose derived data participates in reconstructing a beginning. Temporal closure requires a different condition. Let a finite state be \(S_t\) and let deterministic or explicitly stochastic transition dynamics be \(F\). A conventional period-\(T\) recurrent trajectory satisfies: \[ F^T(S_0) = S_0 \] for some period \(T\). Recurrence alone is still weaker than reciprocal boundary dependence. A replayed loop can return to its initial bytes without its ending causally helping construct its next beginning. Information loss, narrative obligations, and bounded observers are separate properties rather than requirements for cyclic operation. The stronger proposal uses a period-\(T\) history with \(T-1\) ordinary forward transitions and one executed boundary transition. In the proposed twelve-tick world, ordinary forward execution produces states \(S_0\) through \(S_{11}\), and the boundary transition constructs \(S_{12}\). The formal model separates these objects: \[ B_0 = B(S_0) \] where \(B_0\) is a locked projection of beginning requirements fixed before endpoint execution; \[ (S_0,\ldots,S_{T-1}) = F(S_0, A_{0:T-2}) \] where forward dynamics produce the endpoint; \[ E_{T-1} = R(S_{T-1}) \] where \(E_{T-1}\) is the endpoint-derived return value; and: \[ Q_{T-1} = K(S_{T-1}) \] where \(Q_{T-1}\) is the boundary payload. In a lossless arm, \(K\) may preserve a complete checkpoint. In an optional lossy arm, \(K(S_{T-1})=G(D(S_{T-1}))\), where \(D\) creates a genuinely lossy residual and \(G\) produces a reconstructed payload; and: \[ S_T = J(E_{T-1}, L_{T-1}, Q_{T-1}, C) \] where \(J\) is the executed boundary transition, \(L_{T-1}\) is the protected ledger at the endpoint, and \(C\) contains only locked rules and fixed external conditions. Two closure levels must be reported separately: 1. **Requirement-level closure:** \(E_{T-1} = B_0\). 2. **Executed state closure:** the actual boundary transition constructs \(S_T\), after which the locked beginning projection satisfies \(B(S_T) = B_0\). Exact recurrence is a stronger optional condition, \(S_T = S_0\), and must not be inferred from requirement-level closure. The endpoint-derived value must participate in constructing or validating the next state. The initial requirements must be fixed independently before the endpoint is computed. Defining the beginning by applying \(R\) to a chosen ending and then calling the result closure would be circular. Until an ending-derived value participates in an executed boundary transition, the system demonstrates endpoint compatibility rather than an ending that creates its beginning. ## 5. The ending and beginning handshake The phrase "the ending and beginning shake hands" refers to reciprocal boundary dependence. The beginning contributes: - initial identities and relations; - available resources; - unresolved obligations; - permitted actions; - conditions from which the future history develops. The ending contributes: - a return token or reconstructive condition; - fulfilled and unresolved obligations; - stable relation requirements; - retained causal information; - constraints required for the next beginning to be valid. The proposal is not merely that the ending resembles the beginning. It is that the ending carries information used by the executed boundary transition to construct or validate the next beginning, while the beginning generates the history that produces that ending. This dependence must be tested by intervention. If the endpoint token, intermediate action, protected obligation, or required relation is changed, a valid test should detect that the history no longer closes. A structure that closes under every perturbation does not demonstrate meaningful boundary dependence. ## 6. Globally constrained histories The intuitive term "predestined narrative" is translated into a narrower computational statement: > A complete finite history is globally constrained when independently fixed > beginning requirements and ending-derived return requirements admit only a > defined subset of possible histories. This definition does not claim that human lives are predetermined. It does not resolve philosophical disputes about free will. It describes a property of a finite transition system. Suppose a world permits multiple local actions during its expansion phase. The action domain may contain closing and non-closing trajectories. A globally constrained history is one that satisfies the forward rules and the boundary requirements simultaneously. The strength of the constraint can be measured by: - the number of admissible action histories; - the number and proportion of closing histories; - whether closing histories form one primitive cycle or several; - whether endpoint or intermediate interventions destroy closure; - whether non-closing alternatives remain genuinely reachable. If only one action is ever possible, closure may be a scripted artifact. A credible model therefore requires multiple reachable choices and both closing and non-closing histories. ### 6.1 Animus Omega Cycle: optional branch-reconvergence extension The **Animus Omega Cycle**, technically the **Animus Omega branch-reconvergence cycle**, may begin with one authoritative history, create declared represented branches during expansion, reconcile them in stages during contraction, and return to one authoritative history before the next boundary transition. This proposal is an optional stronger version rather than a requirement of an Animus cycle generally. Before execution, the model must freeze the branch origin, branch identities, permitted transitions, merge schedule, conflict rule, and narrative-equivalence projection. That projection states which identities, relationships, obligations, causal dependencies, permissions, ownership, and observer-visible consequences must agree. Branches that agree under this projection are narratively equivalent even when their complete byte states differ. Similarity outside the declared projection cannot justify a merge. “Narrative collapse” is informal shorthand for deterministic semantic reconciliation under those declared invariants. It is not a claim about quantum measurement, physical universes, consciousness, or the destruction of physical realities. Spatial torus topology neither creates temporal branches nor guarantees their reconvergence. Candidate-history enumeration and represented branching are different. Enumeration compares possible complete histories as part of validation. Represented branches coexist as declared states inside one run. Every reconciliation stage must record its input branches, equivalence classes, conflicts, retained invariants, discarded distinctions, canonical output, and provenance. Reconvergence succeeds only when the branch set reaches one canonical history under the frozen rule. It does not establish reciprocal closure by itself. The remaining history must still produce an ending-derived return that satisfies the independently declared beginning contract. If distinct branch states map to one retained state, the reconciliation is many-to-one and information loss is present. Branch-state reduction, information loss, continuity through loss, and reciprocal closure must therefore be tested and reported separately. The browser teaching trace provides an executable illustration of these stages. Its successful reduction is built into the example; it is not Test 05 evidence and does not evaluate reciprocal closure. A future reserved branch-reconvergence experiment is eligible only after a versioned protocol package is deposited with a verifiable time lock. That package must freeze the branch identities and transitions, total narrative-equivalence projection, conflict dispositions, merge schedule, one-history termination rule, resource limits, scoring code, replay count, thresholds, exclusions, and failure rules. Matched controls must detect no-cut credit, hidden trunk copies, scripted convergence, arbitrary deletion, valid equivalent pairs, and unresolved protected conflicts. A failed control invalidates the run family. ## 7. Proposed simulator architecture ### 7.1 Authoritative trunk One canonical state controls the world clock, entity identities, relations, resources, obligations, and accepted events. Observer threads do not write directly to this state. ### 7.2 Observer or region threads Observers receive bounded local views and working memory. Their observations must omit hidden global state, absolute phase labels, and any explicit return marker unless a control arm grants that information. ### 7.3 Protected narrative ledger The protected ledger records high-level information that must remain coherent: - stable identities; - directed and undirected relationships; - permissions and ownership; - promises and obligations; - dependencies between obligations; - deadlines and fulfillment; - unresolved causes; - provenance linking state changes to accepted events. The ledger is not proof of consciousness or personal identity. It is an engineering representation of declared continuity requirements. ### 7.4 Expansion During expansion, the world permits multiple local viewpoints, actions, and microstates. Represented detail and observer-specific state may grow within a fixed resource envelope. Under the optional Animus Omega Cycle extension, a declared origin may also create represented histories with unique branch identities. Observer threads alone do not count as timeline branches. ### 7.5 Contraction and optional dump Contraction does not by itself require information loss. A lossless arm may retain a complete state or checkpoint. In an optional lossy arm, selected microstate is unloaded, summarized, or discarded. That arm's information-loss function must be explicit and non-injective: at least two admissible prior microstates must map to the same retained residual. ### 7.6 Deterministic merge Observer or region proposals are merged under an explicit conflict rule. Accepted events update the authoritative trunk in canonical order. Duplicate, orphaned, contradictory, and stale writes must be detectable. Under the optional Animus Omega Cycle extension, this phase also applies the frozen narrative-equivalence projection and reconciliation rule in declared stages. The branch set must reduce to one canonical history before return. Every stage reports branch counts, equivalence classes, conflicts, discarded distinctions, and provenance. ### 7.7 Reconstruction and return The executed boundary transition combines a boundary payload with the endpoint-derived return value, protected ledger, and locked conditions to construct the next beginning state. A lossless arm may obtain that payload from a complete checkpoint. In an optional lossy arm, the dump function maps the endpoint to a lossy residual and the reconstruction function maps that residual to a reconstructed payload. The endpoint-derived value is compared with independently fixed beginning requirements, and the constructed state's beginning projection is checked against those requirements. ## 8. Optional continuity through information loss This section applies to the optional lossy-continuity hypothesis, not to cyclic closure generally. High-level fidelity cannot mean only "the reconstruction retains whatever was chosen for retention." That would make success tautological. Before execution, a test must identify independently meaningful fields, behaviors, and consequences, such as: - stable identity; - relationship consistency; - obligation fulfillment; - causal dependency order; - access permissions; - resource ownership; - observer-visible consequences; - task completion. Let \(H(S_T)\) be the locked high-level semantic projection of the constructed post-boundary state. Let \(H^*(S_0,\ldots,S_{T-1},B_0)\) be a semantic target fixed by the protocol before confirmatory execution and calculated from independently meaningful history and boundary requirements. A minimal exact-fidelity condition is: \[ H(S_T) = H^*(S_0,\ldots,S_{T-1},B_0) \] This equality must be evaluated while also showing that \(Q_{T-1}=G(D(S_{T-1}))\) contributes to constructing \(S_T\) and that \(D\) discards information. If \(D\) retains every field required to reconstruct the complete endpoint, the test is ordinary lossless checkpointing rather than lossy continuity. Every semantic field must be classified before execution as: - copied directly into the retained ledger or residual; - reconstructed from retained information; - derived by executing post-boundary dynamics; - intentionally discarded. Directly copied ledger fields demonstrate preservation, not reconstruction. The main fidelity test must also evaluate locked downstream behaviors and observer-visible consequences that are not satisfied merely by copying their expected answers into the ledger. Baseline arms must receive the same continuity obligations and must be scored by the same semantic projection. ## 9. Observer boundary indistinguishability The phrase "inhabitants remain unaware" cannot be tested as subjective experience. It is operationalized as a bounded observation claim: > Under a frozen test, a specified decision procedure finds no distinction > meeting its locked criterion between boundary-crossing and matched interior > observation windows for a stated observer class and sampling distribution. Let \(O_i\) be the observation function for observer \(i\). Boundary and interior windows must have equal width and matched phase-relevant conditions. They must exclude absolute tick, hidden global state, and explicit reset labels. Possible measures include: - exact equality of observation-sequence distributions; - total variation distance; - a frozen bounded classifier; - a label-permutation baseline; - per-observer detection rates. The protocol must freeze the window width, sampling process, phase matching, null model, statistic, threshold, uncertainty calculation or exact-enumeration rule, and positive-control acceptance criterion before confirmatory execution. If exact equality is established by exhaustive enumeration, that stronger fact may be reported directly. Otherwise, failure to cross a detection threshold must not be described as proof that observers cannot distinguish the boundary. A full-view observer should serve as a positive control. If no observer, including one given global state and boundary markers, can detect the boundary, the detection test may be defective. Any conclusion applies only to the specified observer class and tested distribution. It does not establish that every possible observer would remain unaware. ## 10. Computational and resource claim The architecture may reduce retained state, but a storage reduction alone is not a computational advantage. Reconstruction, synchronization, and fidelity failures may cost more than the state that was removed. A complete comparison should report: - peak live bytes across the authoritative trunk, ledger, observer buffers, residuals, event logs, checkpoints, and temporary reconstruction state; - cumulative byte-ticks across all arm-specific live storage; - checkpoint or residual size; - deterministic operation count; - dump and reconstruction work; - synchronization and conflict-resolution work; - observer update and observation-generation work; - wall-clock time; - semantic mismatch count; - observer-visible mismatch count; - obligation failures. The primary arm should be compared with: - uninterrupted execution; - ordinary complete checkpoints; - always-expanded lossless execution; - snapshots plus event logs; - an open chain with no return; - no-loss and no-ledger ablations; - a scripted repeating loop; - a compute-matched random ending. Support for a resource hypothesis requires the closure and fidelity gates to pass first. Comparisons must use matched horizons, action histories, semantic obligations, observer-output obligations, and measurement scope wherever the arm permits. Wall time requires a frozen repeated-run method and separate reporting of warmup, number of repetitions, and variation. Support requires a named matched baseline to be beaten on prespecified total-cost criteria, not only checkpoint or residual size. Any supported result would remain limited to the tested finite model. ## 11. Relationship to Tests 01 through 04 ### Test 01: reset-persistence measurement Test 01 validated a method and calibrated a future threshold for measuring selected joint-state dependence after a lossy transformation. It provides measurement ideas for Test 05 but no independent confirmatory coupling effect. ### Test 02: exact bounded primitive closure Test 02 exhaustively enumerated all 66,064 labeled binary relations for state sizes 2, 3, and 4 at periods 1 through 8. It establishes exact bounded facts about primitive cycles. It does not establish an inhabited narrative, causal boundary dependence, or general uniqueness. ### Test 03: carried-state prediction Test 03 asked whether carried recurrent state improved a locked prediction endpoint against an approximately parameter-matched fixed-window model. The criterion failed: \(Q<0\) occurred in 0 of 20 reserved-seed bundles and mean \(Q=0.6826707925423762\). This unsupported result is important negative evidence against assuming that recurrence automatically provides a computational advantage. ### Test 04: exact checkpoint replay Test 04 Revision 1 was operationally aborted and supplies no result. Revision 2 passed all 60 prespecified replay arms under its frozen protocol, with exact immediate restoration and no future semantic-state or observer-output mismatches through tick 4096. Test 04 establishes exact complete-checkpoint replay in one deterministic implementation. It does not establish lossy reconstruction, narrative closure, resource savings, or subjective continuity. ### Foundation, not proof Tests 01 through 04 provide measurement, exact enumeration, negative resource-prediction evidence, replay methods, and evidence-preservation discipline. They do not combine into evidence for the complete Animus Omega conjecture. ## 12. Proposed Test 05 Test 05 is intended to evaluate the conjecture's parts independently in one small deterministic world. Its development plan specifies: - three stable identities; - a four-cell ring; - two bounded radius-one observers; - two directed relationships; - two causally chained obligations; - one contested resource; - a twelve-tick history; - expansion during ticks 3 through 7; - contraction during ticks 8 through 10; - a return boundary at tick 12; - an exhaustive finite action domain containing closing and non-closing histories. The four-cell ring instantiates one spatial topology, and the tick schedule instantiates one expansion and contraction pattern. Without matched non-ring topology arms and alternative phase schedules, Test 05 cannot establish that a ring, expansion, or contraction is necessary or advantageous. Test 05 separates six hypotheses: 1. engineering feasibility; 2. exact reciprocal closure; 3. genuine information loss with bounded semantic fidelity; 4. specified-observer boundary indistinguishability; 5. protected narrative obligation preservation; 6. bounded resource performance against matched baselines. The study remains in development. No valid Test 05 result is reported in this paper. Development output must not be retained as evidence until a documented technical audit confirms that outcomes are calculated from executed arms rather than hard-coded labels or circular definitions. The current design review used an AI architect tool and is not independent peer review. ## 13. Falsification conditions Each Test 05 hypothesis can fail independently in the tested model. Failure of the optional information-loss hypothesis does not by itself refute reciprocal cyclic closure. Examples of component failures include: - no history satisfies independently fixed beginning and ending conditions; - every reachable history closes, making the boundary constraint non-discriminating; - endpoint or intermediate interventions do not break closure; - an arm designated as lossy uses an injective dump and is therefore not genuinely lossy; - high-level obligations fail after reconstruction; - local observers reliably detect the boundary; - the full-view positive control cannot detect the boundary; - resource savings disappear after reconstruction and synchronization costs are counted; - simpler checkpointing or event-sourcing baselines achieve equal fidelity at lower total cost; - results depend on iteration order, undocumented state, or outcome-based exclusions. A mixed result is expected to remain possible. For example, reciprocal closure could succeed in a lossless arm while continuity through loss or the resource comparison fails. Each hypothesis must be reported independently. A separate combined lossy-closure status may be reported, but it must not replace the standalone closure result. ## 14. Alternative explanations and controls A successful result could still have simpler explanations: - a hard-coded loop; - a complete hidden checkpoint; - an observer too weak to detect anything; - a fidelity definition that ignores every discarded field; - an endpoint selected after inspecting outcomes; - a ledger that records obligations but does not affect dynamics; - unmatched resource baselines; - a classifier or threshold selected after seeing confirmatory labels. Required controls must therefore include malformed return data, endpoint interventions, intermediate action changes, ledger deletion, identity shuffling, stale and duplicate events, no-loss execution, full-view observers, ordinary complete checkpoints, and compute-matched non-closing endings. ## 15. Interpretation boundaries Even a fully supported Test 05 would justify only bounded statements such as: - the architecture can be implemented in the tested deterministic model; - an executed ending can satisfy defined conditions required by an independently fixed beginning; - selected high-level invariants can survive a declared lossy transformation; - specified observers did not distinguish the boundary under a frozen test; - the tested implementation had measured costs relative to named baselines. It would not establish: - that the physical universe is a simulation; - that physical time is cyclic; - that consciousness or subjective identity survives a reset; - that inhabitants in general would remain unaware; - that individual lives are predetermined; - that the architecture is generally more efficient; - that Animus Omega is technically novel. Novelty and priority require a comparative literature review. Safety-critical, medical, financial, governmental, transportation, and infrastructure applications require separate domain validation and regulatory analysis. ## 16. Related technical domains Animus Omega combines questions that are already studied separately in distributed systems, checkpointing, event ordering, constraint satisfaction, and time-symmetric boundary models. Similarity to those domains does not establish equivalence or novelty. Distributed snapshot and event-ordering research provides methods for defining consistent states and causal order in systems with multiple processes [1, 2]. Data-system design literature describes logs, state derivation, replication, and recovery patterns relevant to the proposed trunk and ledger [3]. Constraint-processing research provides a general framework for histories restricted by simultaneous conditions [4]. Time-symmetric formulations in physics illustrate the mathematical use of initial and final boundary conditions, but they do not validate the proposed software architecture or any cosmological interpretation [5]. A complete novelty review remains future work. The present paper claims only a specific conjecture and test program. ## 17. Open research questions 1. What is the smallest nontrivial world in which reciprocal closure cannot be reduced to a scripted loop? 2. Which semantic fields are independently meaningful enough to define high-level fidelity? 3. How much information can be removed before obligations or observer-visible consequences fail? 4. Can observer-boundary indistinguishability survive stronger observer classes? 5. Can mutually constrained boundaries coexist with multiple reachable local choices? 6. Does globally constrained closure improve any engineering outcome relative to standard checkpoints, event logs, or state-machine replication? 7. How should reconstruction and synchronization costs be included in total resource accounting? 8. Under what conditions do multiple closing histories exist, and how should one be selected without outcome-dependent bias? ## 18. Evidence and provenance The completed Tests 01 through 04 are preserved separately in the immutable public evidence bundle: `exact-evidence-tests-01-04-2026-09-10.zip` The bundle has its own checksum, manifests, reports, source archives, correction notices, and verification instructions. This preprint does not modify or replace that frozen evidence. No OSF identifier, DOI, or theory-preprint URL is asserted in this version. Add those values only after the relevant service assigns them. ## 19. Funding, interests, and attribution Tests 01 through 04 received no external funding. This theoretical preprint also received no external funding. The author is co-founder of BatchBuddy, a commercial compliance platform, and serves as president of The Love Tower at Ashah, a separate nonprofit. Neither organization funded this work, and neither organization is part of the evidence record. Cholee Hackett is the sole author and accountable contributor. AI systems were used as tools for drafting, code assistance, criticism, and document preparation. They are not authors or independent replicators. ## 20. License Copyright 2026 Cholee Hackett. This author-written theoretical preprint is licensed under the Creative Commons Attribution 4.0 International license. Software, data, binaries, and third-party material retain their own licenses or notices. This narrative license does not automatically relicense them. ## 21. Companion records - *Persistence and Primitive Closure in Finite Computational Systems*: the retrospective Tests 01 through 04 evidence record. - *Test 05 development plan: bounded narrative closure*: the current AI-assisted technically audited design for the combined simulator study. - Future Test 05 prospective registration: to be created only after the implementation, arm matrix, metrics, thresholds, failure rules, and reserved seeds are frozen and time-locked. ## References 1. Chandy, K. M., and Lamport, L. (1985). Distributed snapshots: Determining global states of distributed systems. *ACM Transactions on Computer Systems*, 3(1), 63–75. https://doi.org/10.1145/214451.214456 2. Lamport, L. (1978). Time, clocks, and the ordering of events in a distributed system. *Communications of the ACM*, 21(7), 558–565. https://doi.org/10.1145/359545.359563 3. Kleppmann, M. (2017). *Designing Data-Intensive Applications*. O'Reilly Media. 4. Dechter, R. (2003). *Constraint Processing*. Morgan Kaufmann. 5. Aharonov, Y., Bergmann, P. G., and Lebowitz, J. L. (1964). Time symmetry in the quantum process of measurement. *Physical Review*, 134(6B), B1410–B1416. https://doi.org/10.1103/PhysRev.134.B1410 # OSF update instructions — Animus Omega conjecture preprint version 1.1 **Date:** September 11, 2026 ## Purpose Preprint version 1.0 could be read as making selective information loss and reconstruction necessary for cyclic closure. Version 1.1 corrects that interpretation: > A bounded simulation may operate cyclically without discarding lower-level > detail. Reciprocal closure asks whether the ending helps construct the next > beginning while that beginning produces the ending. Continuity through > information loss is a separate, optional, stronger question. ## OSF action Do not silently replace or delete version 1.0 if it is already public. 1. Add the version 1.1 PDF as a new version or dated file. 2. Add the dated correction notice: `animus-omega-conjecture-v1.1-correction-2026-09-11.md`. 3. Replace the displayed abstract with the version 1.1 abstract in `ANIMUS_OMEGA_CONJECTURE_OSF_UPLOAD.md` if the OSF interface allows metadata updates. 4. Keep version 1.0 available in version history. 5. State that the correction changes no completed Test 01–04 evidence and reports no Test 05 result. ## Files to upload - `Animus-Omega-Conjecture-Preprint-v1.1.pdf` - `Animus-Omega-Conjecture-Preprint-v1.1.pdf.sha256` - `animus-omega-conjecture-v1.1-correction-2026-09-11.md` ## Scope This is a correction to explanatory theory language. It does not alter any frozen protocol, source code, seed, checkpoint, result, exclusion, or evidence status from Tests 01–04. # Claims not made by the Animus-cycle specification **Status:** companion claims boundary for the proposed design specification, version 1.0, 2026-09-11. The Animus-cycle specification and its frozen reference fixtures do not establish: - legal exclusivity over the words “Animus cycle”; - legal exclusivity over the proposed design name “Animus Omega Cycle”; - priority over checkpointing, event sourcing, deterministic replay, fixed-point constraints, self-consistency constraints, bounded-observer models, or state reconstruction; - that the complete architecture is scientifically or technically novel; - that naming the optional branch-reconvergence version “Animus Omega Cycle” establishes novelty, priority, implementation, or validation; - that a documented negative systematic search establishes the complete conjunction is absent from prior systems; - that Tests 01–04 establish an Animus cycle; - a Test 05 result; - physical recurrence or a cyclic physical universe; - that spatial torus topology creates temporal branches or forces them to reconverge; - that candidate enumeration, observer threads, an always-single trunk, branch deletion, or scripted equal outputs demonstrate represented branch reconvergence; - that branch-set reduction by itself establishes preservation of protected semantics, deterministic replay, or reciprocal closure; - that a successful branch-reconvergence fixture establishes that arbitrary branches can reconcile, that one history is physically real, or that physical alternatives cease to exist; - that “narrative collapse” describes quantum measurement, physical realities, or the destruction of universes; - consciousness, subjective continuity, or observer indistinguishability; - unrestricted predestination or information arriving from an unconstrained future; - entropy removal, information creation, or exact recovery after a lossy transformation; - general computational, memory, energy, or resource advantage; - that every ledger-free architecture must fail; - that provenance labels or authored-at metadata prove ending authorship; - that writer eligibility implies intention, awareness, or motive; - that a protected ledger alone establishes continuity through information loss; or - that a local draft has an OSF identifier, DOI, publication date, or Registration status. The reference fixtures are executable teaching examples. Their PASS and FAIL values are conditional on their frozen candidate domain, contracts, reconstruction rules, observer model, interventions, and validator. Any future reserved branch-reconvergence result is conditional on its prospectively time-locked fixtures, branch schema, transition table, narrative-equivalence projection, conflict rules, merge schedule, controls, thresholds, exclusions, and failure rules. Changing any of those after inspection of reserved outcomes creates a new protocol; it cannot rescue or reinterpret the original run. Tests 01–04 remain separate retrospective studies with their original scopes, outcomes, deviations, and limitations. Test 03 remains unsupported. Test 04 Revision 1 remains aborted. Test 04 Revision 2 is limited to exact replay in its fixed deterministic model.