{
  "title": "Persistence and Primitive Closure in Finite Computational Systems",
  "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.",
    "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.",
      "recurrent_state": "Carried state may improve prediction under resource constraints; the direct pilot remains non-evidence until its mandatory gate and reserved-seed execution pass.",
      "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."
    },
    "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.",
      "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": "Pending/non-evidence. The implementation has not passed the mandatory independent code gate; no confirmatory manifest was created and reserved seeds were not accessed."
    }
  ],
  "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"
  ]
}