{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__music_musicology","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"music_musicology","decision":"CANDIDATE","problem_id":"universal_generative_score_motif_reachability","causal_lever_id":"enforceable_score_fragment_with_labeled_fallbacks","proposal":{"problem":"Can a music-analysis service correctly decide, and terminate, for every score in an open-ended executable generative-music language whether its performance will ever emit a specified motif or musical event? The independently recognizable failure is treating timeout as absence or promising universal analysis without defining the score language and guarantee.","actors_substrate":["composers and generative-score authors","music-information-retrieval engineers","musicologists and cataloguers","performers and automated playback services","executable scores, interpreters, and event streams"],"observable_state":"Some valid score-event queries yield confirmed reachability, while others time out, run indefinitely, or receive Boolean answers unsupported by a class-wide termination argument.","consequence":"Potentially false motif classifications, hanging analysis jobs, misleading catalog records, and continued investment in an impossible unrestricted analyzer.","affected_objective":"Provide useful automated score analysis without overstating reachability, absence, or termination guarantees.","structural_mapping":[{"archetype_element":"open-ended problem class","domain_realization":"Executable generative scores paired with a formally encoded target motif or event.","claim_kind":"INFERENCE"},{"archetype_element":"universal exact terminating requirement","domain_realization":"One analyzer must return YES or NO for every well-formed score-event pair and always halt.","claim_kind":"INFERENCE"},{"archetype_element":"computability boundary","domain_realization":"If the score language can express unrestricted computation, motif emission may encode whether a computation halts.","claim_kind":"HYPOTHESIS"},{"archetype_element":"decidable region","domain_realization":"Finite-state scores, bounded performances, or a mechanically enforced terminating score fragment.","claim_kind":"INFERENCE"},{"archetype_element":"honest fallback","domain_realization":"Witness-backed YES, bounded UNKNOWN, sound abstraction, or explicit out-of-scope status instead of timeout-as-NO.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Problem-Class Specification","status":"adapted","domain_realization":"Define score-event reachability over a named generative-score language."},{"component":"Instance Representation Contract","status":"adapted","domain_realization":"Versioned score syntax, interpreter semantics, motif encoding, and initial state."},{"component":"Computation Model Contract","status":"adapted","domain_realization":"Fix interpreter, event-stream behavior, nondeterminism, and external inputs."},{"component":"Solvability Guarantee Profile","status":"direct","domain_realization":"Distinguish total decision, recognition, bounded result, and abstraction."},{"component":"Quantifier and Scope Map","status":"direct","domain_realization":"Separate every score from individual scores and bounded corpora."},{"component":"Computability Status Lattice","status":"direct","domain_realization":"Classify fragments as decidable, recognizable, relative, or unresolved."},{"component":"Constructive Procedure Witness","status":"adapted","domain_realization":"Require algorithm plus correctness and termination proof for claimed fragments."},{"component":"Reduction Preservation Contract","status":"adapted","domain_realization":"Specify a computable map from machine instances to scores preserving motif reachability."},{"component":"Computability Impossibility Certificate","status":"adapted","domain_realization":"Retain a checked reduction proof before declaring the unrestricted class undecidable."},{"component":"Assumption Register","status":"direct","domain_realization":"Record expressiveness, semantics, target equality, and environmental assumptions."},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"Map finite-state, structurally terminating, and bounded-performance score classes."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"Confirm reachability only when a target-event trace is witnessed."},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"Keep UNKNOWN, timeout, out-of-scope, and NO distinct."},{"component":"Fallback Solution Contract","status":"direct","domain_realization":"Route to exact, abstract, bounded, recognizer, or human-review modes with labels."},{"component":"Computability Guarantee Record","status":"direct","domain_realization":"Publish the precise guarantee beside each result."},{"component":"Recheck Trigger","status":"adapted","domain_realization":"Reclassify after language, interpreter, plug-in, or external-input changes."},{"component":"Termination Condition","status":"direct","domain_realization":"Set explicit step, event, depth, or time bounds for fallback execution."},{"component":"Scope Boundary","status":"direct","domain_realization":"Mechanically accept the supported fragment and quarantine the rest."},{"component":"Decision Record","status":"direct","domain_realization":"Version the selected boundary, evidence, and shipped modes."},{"component":"Uncertainty Residue","status":"direct","domain_realization":"List unproved reduction obligations and unresolved fragments."},{"component":"Independent Proof Review","status":"direct","domain_realization":"Have an independent reviewer check formalization and proofs."},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"Assess runtime and state explosion only after decidability is established."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Over-approximate reachable musical-event states; report its one-sided guarantee.","counterfactual_removal":"Removes a sound finite-state fallback for some unbounded scores."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Exhaust events or states only within an explicit bound.","counterfactual_removal":"Eliminates complete bounded verdicts and boundary tests."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version score scope, guarantee, evidence, and recheck triggers.","counterfactual_removal":"Boundary and labels can drift silently."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Gate feasibility analysis after a fragment is shown decidable.","counterfactual_removal":"Decidable but unusable modes may ship."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Certify exact analyzers for restricted score fragments.","counterfactual_removal":"Positive decidability claims lack total witnesses."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A valid halting reduction is more direct for this encoded target.","counterfactual_removal":"No change if the reduction certificate remains."},{"slug":"enumeration_and_dovetailing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Deterministic score simulation already recognizes a witnessed event; dovetailing is unnecessary unless nondeterminism requires it.","counterfactual_removal":"No change for the initial deterministic scope."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Dispatch exact, abstract, bounded, and UNKNOWN modes with guarantee labels.","counterfactual_removal":"Weaker outputs can be mistaken for universal decisions."},{"slug":"halting_problem_reduction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Attempt a computable translation whose score emits the motif iff the source computation halts.","counterfactual_removal":"The proposed unrestricted impossibility boundary loses its evidence."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Enforce a syntactic score fragment admitting total reachability analysis.","counterfactual_removal":"There is no enforceable exact-answer region."},{"slug":"many_one_reduction_proof","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Discharge totality, computability, and answer preservation of the halting map.","counterfactual_removal":"The impossibility transfer may be invalid."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"An unenforced promise permits authoritative answers on violating scores; use checkable syntax instead.","counterfactual_removal":"No change because fragment membership supplies the boundary."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use one in-scope looping or misclassified score to refute an existing universal implementation claim.","counterfactual_removal":"Cheap falsification of over-broad claims is lost."},{"slug":"proof_checking","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently verify the fragment proof and impossibility certificate.","counterfactual_removal":"A subtle proof gap could govern deployment."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Require known-undecidable source to target score-reachability direction.","counterfactual_removal":"A reversed reduction could falsely establish impossibility."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Return witnessed YES or bounded UNKNOWN, never timeout-as-NO.","counterfactual_removal":"The operational system recreates the deceptive Boolean failure."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Optional proof discovery adds no necessary role to the bounded first test.","counterfactual_removal":"Manual independent proof review remains sufficient."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Relative degrees and adaptive oracles exceed the flat boundary question.","counterfactual_removal":"No material change to the proposed classification."}],"causal_chain":["[HYPOTHESIS] The unrestricted score language can encode arbitrary computation.","A checked source-to-score construction makes target-event reachability reveal halting.","If preservation holds, a total exact reachability analyzer would decide the source contradiction.","An enforceable terminating fragment restores exact decisions for admitted scores.","A labeled router sends other scores to sound abstraction or witnessed-YES/bounded-UNKNOWN modes.","Versioned records and recheck triggers prevent weaker guarantees from becoming universal claims."],"baseline":"Baseline under test: run the score analyzer until a timeout, treat observed emission as YES and exhaustion as NO, with ad hoc manual review of failures.","nearest_rival":"Treat all valid scores as bounded by a product performance horizon and use exhaustive simulation; this is simpler but answers only bounded-horizon reachability, not eventual reachability.","authority_safety":{"affected_parties":["score authors","performers","catalogue users","analysts","listeners represented by motif labels"],"decision_authority":"The analysis-service owner may define product guarantees and supported syntax; score authors retain authority over works and intended musical meaning.","authorized_first_step":"Offline shadow test on synthetic score-event pairs covering terminating, looping, out-of-fragment, abstraction, and reduction-gadget cases; publish no catalog verdicts.","excluded_actions":["altering or suppressing compositions","claiming aesthetic or cultural meaning from formal reachability","converting UNKNOWN or timeout to NO","deploying an unchecked impossibility claim"],"halt_rollback":"Halt if any supposedly exact fragment yields a wrong answer, the checker rejects a proof, the reduction obligation fails, or UNKNOWN is collapsed downstream; withdraw the affected guarantee and revert to labeled UNKNOWN/manual review."}},"negative_tests":{"strongest_counterevidence":"[HYPOTHESIS] Most operational generative-score formats may already impose finite timelines, bounded loops, or finite-state controls; then exhaustive reachability is computable and the real issue is complexity.","analogy_break":"A formal emitted motif is not musical significance: listener perception, performance practice, variation, and cultural identity may not admit the fixed encoding required by the reduction. The boundary applies only to the encoded event property.","failure_condition":"The proposal fails if the declared score language cannot express the reduction gadgets, fragment membership is not enforceable, or fallback labels are lost by downstream systems.","problem_falsifier":"Show that the actual claimed input class is finite or governed by a known total interpreter and that no universal eventual-reachability claim is made; observed delays would then indicate scaling, not a computability-boundary problem.","intervention_falsifier":"After contracts are fixed, produce an independently checked total and correct decider for the full declared class, or show the proposed source-to-score map is noncomputable or fails answer preservation.","risks":["A proof about the wrong score semantics could falsely retire feasible work.","A restrictive fragment could exclude musically important generative practices.","False alarms from abstraction could burden authors or reviewers.","Bounded results could be laundered into claims beyond the horizon.","Formal motif equality could encode culturally inappropriate classifications."]},"null_rationale":null,"classification":{"candidate_kind":"TESTABLE_CONJECTURE","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":0.78,"generator_notes":"Closed-book structural transfer. The unrestricted-language expressiveness and halting-preserving translation are hypotheses requiring formal construction and independent checking; no prior-art claim is made."}