{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__linguistics_semiotics","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"linguistics_semiotics","decision":"CANDIDATE","problem_id":"unbounded_grammar_equivalence_total_decider_requirement","causal_lever_id":"grammar_equivalence_solvability_boundary_and_honest_fallback","proposal":{"problem":"A grammar workbench is required to decide, for every pair of grammars expressible in an extensible generative formalism, whether they generate exactly the same strings, always terminating with YES or NO. The formalism, encoding, quantifier scope, and treatment of timeouts are not fixed, so implementation failures are being mistaken for evidence about universal solvability.","actors_substrate":["formal linguists and grammar authors","language-tool engineers","reviewers of grammar revisions","downstream users relying on equivalence verdicts"],"observable_state":"Tests succeed on small grammars, but larger or newly expressive grammars time out; the interface nevertheless forces a Boolean verdict, and documentation retains an unrestricted equivalence claim.","consequence":"Equivalent grammars may be rejected, inequivalent grammars approved, or effort repeatedly invested in a total analyzer that may not exist for the declared class.","affected_objective":"Trustworthy, terminating comparison and change control for formal grammars.","structural_mapping":[{"archetype_element":"universal exact terminating requirement","domain_realization":"Exact language-equivalence verdict for every grammar pair","claim_kind":"INFERENCE"},{"archetype_element":"implicit problem class and encoding","domain_realization":"Extensible grammar syntax and string semantics lack a versioned contract","claim_kind":"INFERENCE"},{"archetype_element":"constructive-versus-impossibility evidence","domain_realization":"Seek a total equivalence algorithm and a valid undecidability reduction in parallel","claim_kind":"HYPOTHESIS"},{"archetype_element":"restricted decidable region","domain_realization":"Mechanically enforceable grammar fragments with proved decision procedures","claim_kind":"HYPOTHESIS"},{"archetype_element":"honest weaker fallback","domain_realization":"Witness-based inequivalence, bounded comparison, or UNKNOWN instead of fabricated NO","claim_kind":"HYPOTHESIS"},{"archetype_element":"reclassification trigger","domain_realization":"New grammar operators, semantics, or external capabilities reopen the boundary decision","claim_kind":"HYPOTHESIS"}],"component_map":[{"component":"Problem-Class Specification","status":"adapted","domain_realization":"Pairs of grammars and exact language equivalence"},{"component":"Instance Representation Contract","status":"adapted","domain_realization":"Versioned grammar and alphabet encoding"},{"component":"Computation Model Contract","status":"direct","domain_realization":"Effective machine, resources, and permitted services"},{"component":"Solvability Guarantee Profile","status":"direct","domain_realization":"Exact-total, recognizing, bounded, or approximate"},{"component":"Quantifier and Scope Map","status":"direct","domain_realization":"Every grammar pair versus named fragments"},{"component":"Computability Status Lattice","status":"direct","domain_realization":"Decidable through unresolved statuses"},{"component":"Constructive Procedure Witness","status":"adapted","domain_realization":"Equivalence decider plus proof"},{"component":"Reduction Preservation Contract","status":"adapted","domain_realization":"Computable source-to-grammar encoding preserving answers"},{"component":"Computability Impossibility Certificate","status":"adapted","domain_realization":"Checked proof for the exact grammar class"},{"component":"Assumption Register","status":"direct","domain_realization":"Syntax, semantics, model, and promise assumptions"},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"Enforceable grammar fragments"},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"Confirmed witness without universal negative"},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"UNKNOWN distinct from NO and failure"},{"component":"Fallback Solution Contract","status":"adapted","domain_realization":"Bounded or one-sided comparison labels"},{"component":"Computability Guarantee Record","status":"direct","domain_realization":"Version-linked public guarantee"},{"component":"Recheck Trigger","status":"adapted","domain_realization":"Grammar-language or model change"},{"component":"Termination Condition","status":"direct","domain_realization":"Proof of totality or explicit resource bound"},{"component":"Scope Boundary","status":"direct","domain_realization":"Accepted fragment and rejected inputs"},{"component":"Decision Record","status":"direct","domain_realization":"Auditable boundary choice"},{"component":"Uncertainty Residue","status":"direct","domain_realization":"Open proof obligations"},{"component":"Independent Proof Review","status":"direct","domain_realization":"Separate checking of boundary evidence"},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"Feasibility analysis after decidability"}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No sound grammar-equivalence abstraction is supplied.","counterfactual_removal":"No change."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Exhaust grammar pairs only within declared size and derivation bounds.","counterfactual_removal":"The pilot loses a complete bounded check."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Record class, guarantee, evidence, and triggers.","counterfactual_removal":"Boundary provenance can drift."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Assess scaling only after a total procedure is proved.","counterfactual_removal":"Decidable may be mistaken for deployable."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Positive branch requires an exhibited total correct decider.","counterfactual_removal":"Decidability could be asserted from examples alone."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A domain-specific direct diagonal construction is not supplied.","counterfactual_removal":"Reduction branch remains."},{"slug":"enumeration_and_dovetailing","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Fairly search candidate distinguishing strings or certificates where recognizable.","counterfactual_removal":"The one-sided fallback lacks a completeness basis."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Route by fragment and label exact, bounded, witness, or UNKNOWN.","counterfactual_removal":"Weaker results can be laundered as equivalence verdicts."},{"slug":"halting_problem_reduction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Attempt a computable answer-preserving encoding into the exact target class.","counterfactual_removal":"There is no decisive negative branch."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Define enforceable syntax admitting a proved decider.","counterfactual_removal":"No guaranteed-answer region can be recovered."},{"slug":"many_one_reduction_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Its obligations are incorporated in the selected halting reduction.","counterfactual_removal":"No material change."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unchecked promises are less safe than enforceable syntax.","counterfactual_removal":"No change."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use an in-scope grammar pair to refute an overbroad analyzer claim.","counterfactual_removal":"Cheap falsification of universality is lost."},{"slug":"proof_checking","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently check the exact theorem and assumptions.","counterfactual_removal":"A flawed or mismatched proof may govern deployment."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Gate source-to-target direction and preservation obligations.","counterfactual_removal":"A reversed reduction may be accepted."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Bound recognition and emit UNKNOWN, never an inferred NO.","counterfactual_removal":"Termination pressure recreates false negatives."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Optional tooling, not necessary for the first boundary test.","counterfactual_removal":"Hand-checkable certificates remain possible."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Relative degrees do not answer the required standalone guarantee.","counterfactual_removal":"No change."}],"causal_chain":["Fix the grammar class, representation, semantics, computation model, and universal guarantee.","Pursue a proved total decider and a valid impossibility reduction as competing classifications.","Independently check whichever evidence closes under the stated assumptions.","For unresolved or excluded cases, route to enforced fragments, bounded checks, witness search, or UNKNOWN.","Publish guarantee labels and recheck when expressiveness or assumptions change."],"baseline":"Build a heuristic equivalence checker, benchmark finite examples, retry timeouts, and force unresolved cases into YES or NO.","nearest_rival":"Complexity scaling assessment, appropriate only if a total algorithm for the actual class is already established.","authority_safety":{"affected_parties":["grammar authors whose work is accepted or rejected","engineers maintaining analyzers","users relying on equivalence claims"],"decision_authority":"The grammar-tool owner may authorize an isolated classification pilot; changing production verdicts requires formal-methods review and affected-user approval.","authorized_first_step":"Freeze one versioned grammar formalism; analyze 20 representative pairs and all pairs within a small declared bound; attempt both a constructive proof and a source-to-target reduction; expose results only as pilot evidence.","excluded_actions":["Declare undecidability from timeout or failed proof search","Generalize bounded results past their fence","Silently narrow accepted grammar syntax","Use UNKNOWN as NO in production"],"halt_rollback":"Stop the pilot if encoding fidelity is disputed, a proof obligation fails review, or any result escapes its label; withdraw the boundary record and restore prior non-authoritative behavior."}},"negative_tests":{"strongest_counterevidence":"A uniform algorithm with independently checked correctness and termination proofs for every grammar pair in the actual extensible formalism would defeat the diagnosis and redirect work to complexity.","analogy_break":"Grammars are not automatically programs: a halting reduction fails unless its computable encoding preserves the exact generated-language equivalence question under the deployed semantics.","failure_condition":"The mapping fails if the real requirement concerns only a fixed finite grammar set, or if the formalism is already an enforceable fragment with a proved total decider.","problem_falsifier":"Audit shows no universal total claim: every accepted grammar lies in a mechanically enforced, proved-decidable fragment and UNKNOWN is already preserved.","intervention_falsifier":"After fixing faithful contracts, neither a checked total procedure nor a checked impossibility result is obtained, and proposed restricted or one-sided modes provide no useful coverage at acceptable error and UNKNOWN rates.","risks":["A formal model may omit pragmatic or contextual meaning relevant to users.","A restriction may remove linguistically important constructions.","Bounded success may be misreported as universal evidence.","Frequent UNKNOWN may shift unaudited decisions to humans.","An incorrect reduction or proof may prematurely terminate useful research."]},"null_rationale":null,"classification":{"candidate_kind":"DOMAIN_TRANSFER","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":0.86,"generator_notes":"Closed-book structural inference. Target-specific decidability and reduction claims remain hypotheses pending formalization and independent proof review."}