{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__cognitive_science","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"cognitive_science","decision":"CANDIDATE","problem_id":"universal_cognitive_model_equivalence_claim","causal_lever_id":"scoped_equivalence_with_explicit_unknown","proposal":{"problem":"Cognitive-modeling projects may require an analyzer that always terminates and decides whether any two arbitrary executable cognitive models predict identical behavior for every possible stimulus history. Passing benchmarks, timeouts, or failure to find a distinguishing experiment can then be misreported as universal equivalence, despite an unstated model language, horizon, and treatment of nontermination.","actors_substrate":["computational cognitive scientists","model authors","experimental designers","reviewers","downstream users of model-comparison claims","executable cognitive models and experiment generators"],"observable_state":"A Boolean equivalent/not-equivalent verdict is issued for open-ended executable models without an enforceable class boundary, totality argument, or UNKNOWN state; finite test agreement is presented as universal predictive equivalence.","consequence":"Distinct models can be declared interchangeable, or a potentially impossible universal analyzer can absorb continued engineering effort, while restricted or one-sided evidence is overstated.","affected_objective":"Produce auditable model-comparison claims that distinguish universal equivalence from bounded agreement, witnessed inequivalence, and unresolved cases.","structural_mapping":[{"archetype_element":"unrestricted decision class","domain_realization":"Pairs of executable cognitive models quantified over every permitted stimulus history and execution length.","claim_kind":"INFERENCE"},{"archetype_element":"total exact decider requirement","domain_realization":"The analyzer must always halt and return whether all predictions coincide.","claim_kind":"INFERENCE"},{"archetype_element":"impossibility boundary","domain_realization":"If the model language can encode unrestricted computation, universal behavioral equivalence may admit a halting-problem reduction.","claim_kind":"HYPOTHESIS"},{"archetype_element":"decidable region","domain_realization":"Mechanically enforceable finite-state languages, bounded horizons, and finite stimulus alphabets permit exhaustive comparison in principle.","claim_kind":"INFERENCE"},{"archetype_element":"honest fallback","domain_realization":"Return witnessed INEQUIVALENT, bounded-equivalent, or UNKNOWN with the applicable scope attached.","claim_kind":"HYPOTHESIS"}],"component_map":[{"component":"Problem-Class Specification","status":"direct","domain_realization":"Define model pairs, observable predictions, stimulus histories, and equivalence relation."},{"component":"Instance Representation Contract","status":"direct","domain_realization":"Version model syntax, stimulus encoding, initial state, and output trace semantics."},{"component":"Computation Model Contract","status":"direct","domain_realization":"State whether models are finite-state, Turing-complete, stochastic, interactive, or oracle-assisted."},{"component":"Solvability Guarantee Profile","status":"direct","domain_realization":"Separate universal equivalence, witnessed inequivalence, bounded agreement, and UNKNOWN."},{"component":"Quantifier and Scope Map","status":"direct","domain_realization":"Expose quantification over model pairs, stimuli, random seeds, and time."},{"component":"Computability Status Lattice","status":"adapted","domain_realization":"Classify each comparison regime as decidable, recognizable on one side, relative, or unresolved."},{"component":"Constructive Procedure Witness","status":"direct","domain_realization":"Provide the terminating comparison algorithm for each restricted class."},{"component":"Reduction Preservation Contract","status":"direct","domain_realization":"Specify a computable encoding from halting instances to model pairs and preserve the equivalence answer."},{"component":"Computability Impossibility Certificate","status":"direct","domain_realization":"Retain the checked reduction for the unrestricted claim."},{"component":"Assumption Register","status":"direct","domain_realization":"Record expressiveness, determinism, observability, and input-generation assumptions."},{"component":"Decidable Subclass Map","status":"direct","domain_realization":"Map enforceable finite-state and bounded-horizon fragments."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"A finite distinguishing trace certifies inequivalence; lack of one does not certify equivalence."},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"Keep UNKNOWN, timeout, out-of-scope, and equivalent distinct."},{"component":"Fallback Solution Contract","status":"direct","domain_realization":"Route to exact restricted comparison, bounded search, or witness search with labeled guarantees."},{"component":"Computability Guarantee Record","status":"direct","domain_realization":"Link each released verdict type to its class, proof, and limits."},{"component":"Recheck Trigger","status":"direct","domain_realization":"Reclassify when model syntax, observables, horizon, oracle access, or randomness changes."},{"component":"Termination Condition","status":"direct","domain_realization":"Finite enumeration completion or declared time/state/depth budget."},{"component":"Scope Boundary","status":"direct","domain_realization":"Mechanically reject or quarantine models outside the certified fragment."},{"component":"Decision Record","status":"direct","domain_realization":"Record the selected comparison mode and reason per model pair."},{"component":"Uncertainty Residue","status":"direct","domain_realization":"List unproved reduction obligations, abstraction gaps, and UNKNOWN cases."},{"component":"Independent Proof Review","status":"direct","domain_realization":"A reviewer checks theorem statement, formalization, and reduction direction."},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"After decidability, assess state-space growth and practical feasibility."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A one-directional safety abstraction does not directly establish symmetric behavioral equivalence; defer unless a suitable relation-preserving abstraction is proved.","counterfactual_removal":"No change to the proposed core boundary or pilot."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Enumerate all model states and stimuli within enforced finite bounds.","counterfactual_removal":"The bounded-equivalent verdict loses its completeness basis."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version the chosen boundary, shipped labels, assumptions, and recheck triggers.","counterfactual_removal":"The mathematics remains, but guarantee drift becomes unauditable."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Measure state-space growth only after a restricted comparison is shown decidable.","counterfactual_removal":"The pilot could confuse decidability with usable runtime."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Supply termination and correctness proofs for the finite-fragment comparator.","counterfactual_removal":"Restricted exactness would rest only on testing."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A direct diagonal proof is unnecessary if the narrower reduction obligation succeeds.","counterfactual_removal":"No change because it is not used."},{"slug":"enumeration_and_dovetailing","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Fairly interleave simulations to seek finite distinguishing traces across candidate experiments.","counterfactual_removal":"Witness discovery can be starved by a nonterminating simulation."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Dispatch enforceably in-scope pairs to exact comparison and others to bounded or witness-search modes.","counterfactual_removal":"Weaker evidence can again be presented under one Boolean label."},{"slug":"halting_problem_reduction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Attempt a computable encoding showing that unrestricted equivalence would decide halting.","counterfactual_removal":"There is no principled basis for rejecting the universal total analyzer."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Use a parser/type discipline to enforce a finite-state cognitive-model fragment.","counterfactual_removal":"The exact-decider scope cannot be reliably policed."},{"slug":"many_one_reduction_proof","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Formalize the halting reduction as a total computable answer-preserving map.","counterfactual_removal":"The impossibility argument risks remaining a loose analogy."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unenforced promises permit authoritative outputs on violations; syntactic fragment enforcement is safer.","counterfactual_removal":"No change to the enforceable scope boundary."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use one verified distinguishing experiment to refute universal equivalence claims.","counterfactual_removal":"Inequivalence remains discoverable, but the cheapest decisive test is lost."},{"slug":"proof_checking","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently verify the restricted decider proof and impossibility certificate against the stated semantics.","counterfactual_removal":"A formalization or proof gap could authorize a false boundary."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Confirm the map runs from halting to cognitive-model equivalence and names all assumptions.","counterfactual_removal":"A reversed or incomplete reduction may be accepted."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"After a declared budget, return UNKNOWN unless a distinguishing witness was checked.","counterfactual_removal":"Timeouts are likely to be laundered into equivalence."},{"slug":"theorem_prover_guided_search","disposition":"unused","contribution_type":"NONE","adaptation_or_rejection":"Machine-assisted discovery is optional and cannot substitute for correct cognitive semantics.","counterfactual_removal":"Independent checking and the bounded pilot remain viable."},{"slug":"turing_reduction_analysis","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Relative computability degrees are unnecessary for the binary boundary and obscure the desired one-map preservation claim.","counterfactual_removal":"No loss to the proposed classification."}],"causal_chain":["Specify executable models, observations, computation model, and universal quantifiers.","Attempt and independently check a halting-to-equivalence reduction for the unrestricted class.","Enforce a finite decidable fragment and prove its comparator total and correct.","Route each pair by class: exact restricted comparison, bounded exhaustive comparison, or fair witness search.","Attach EXACT, BOUNDED, WITNESSED-INEQUIVALENT, OUT-OF-SCOPE, or UNKNOWN to every result.","Recheck the boundary when model expressiveness or experimental semantics changes."],"baseline":"Compare models on a finite benchmark suite; treat agreement as equivalence and timeout or search exhaustion as no difference found.","nearest_rival":"Simply enlarge the benchmark suite and use randomized differential testing without classifying what its negative result guarantees.","authority_safety":{"affected_parties":["model authors whose theories may be merged or rejected","experimental participants indirectly affected by study design","reviewers and readers relying on equivalence claims","downstream researchers reusing models"],"decision_authority":"The study's designated methods lead may authorize labels only after an independent formal-methods reviewer approves the representation contract and proof obligations; scientific equivalence claims remain subject to normal review.","authorized_first_step":"On synthetic model pairs only, classify 20 pairs into an enforced finite fragment or out-of-scope; compare router labels against the ordinary benchmark baseline and retain all witnesses and UNKNOWN outcomes.","excluded_actions":["Do not relabel existing published models as equivalent or invalid.","Do not deploy the analyzer for clinical, personnel, educational, or participant-level decisions.","Do not report timeout, bounded agreement, or UNKNOWN as universal equivalence.","Do not infer facts about human minds beyond the formal model semantics."],"halt_rollback":"Halt if the fragment checker admits an out-of-class model, any exact verdict lacks a replayable certificate, the reviewed reduction fails, or labels are collapsed downstream. Withdraw universal claims, preserve results as bounded observations, and revert to explicit human review."}},"negative_tests":{"strongest_counterevidence":"The actual cognitive-model language may be finite-state with a fixed finite stimulus set and horizon; then exact equivalence is already decidable and the unrestricted-boundary diagnosis is misplaced.","analogy_break":"Executable cognitive models are scientific representations, not automatically arbitrary programs; a computability theorem transfers only if their permitted syntax and observational semantics support the required encoding.","failure_condition":"The intervention fails if enforceable restrictions exclude most scientifically relevant models or produce UNKNOWN so often that researchers bypass the router.","problem_falsifier":"The problem is falsified if stakeholders require claims only over a declared finite experiment set and consistently label them as bounded agreement, with no universal exact-termination requirement.","intervention_falsifier":"In the bounded pilot, the router is falsified as useful if it does not reduce unsupported equivalence labels versus baseline, emits any false exact verdict, or cannot mechanically enforce its fragment.","risks":["A checked proof may formalize the wrong notion of cognitive prediction.","Restrictions may privilege conveniently formalized theories and distort scientific comparison.","Official guarantee labels may create unwarranted trust.","State-space explosion may make a decidable fragment operationally useless.","A finite distinguishing trace may reflect encoding artifacts rather than a meaningful theoretical difference."]},"null_rationale":null,"classification":{"candidate_kind":"MECHANISM_COMPOSITION","prior_art_status":"UNSEARCHED","evidence_maturity":"HYPOTHESIS"},"revision_change_log":{"revision_kind":"ORIGINAL","prior_problem_id":null,"prior_causal_lever_id":null,"problem_changed":false,"causal_lever_changed":false,"conceptual_changes":[],"operational_changes":[],"repairs_addressed":[]},"confidence":0.84,"generator_notes":"Closed-book structural transfer. The central undecidability claim is explicitly hypothetical until the cognitive-model language, observational semantics, and reduction are formalized and independently checked."}