Animus Omega Preprint v1.0

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:

The simulation may use a periodic spatial topology.
Independently of spatial topology, its complete history may satisfy a temporal closure condition.
Its represented world expands, reaches a defined limit, contracts, and begins again.
The transition from ending to beginning is causally coherent.
The ending creates or carries conditions required by the beginning.
Forward execution from the beginning eventually creates that ending.
Beginning and ending are mutually constrained because each participates in the conditions that make the other possible.
Complete histories must satisfy both independently specified beginning requirements and ending-derived return requirements.
Only histories consistent with the full cycle qualify as closing histories.
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.
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:

Requirement-level closure: (E_{T-1} = B_0).
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:

engineering feasibility;
exact reciprocal closure;
genuine information loss with bounded semantic fidelity;
specified-observer boundary indistinguishability;
protected narrative obligation preservation;
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

What is the smallest nontrivial world in which reciprocal closure cannot be reduced to a scripted loop?
Which semantic fields are independently meaningful enough to define high-level fidelity?
How much information can be removed before obligations or observer-visible consequences fail?
Can observer-boundary indistinguishability survive stronger observer classes?
Can mutually constrained boundaries coexist with multiple reachable local choices?
Does globally constrained closure improve any engineering outcome relative to standard checkpoints, event logs, or state-machine replication?
How should reconstruction and synchronization costs be included in total resource accounting?
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

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.

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