{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__art_aesthetics","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"art_aesthetics","decision":"CANDIDATE","problem_id":"universal_generative_art_output_certification","causal_lever_id":"restrict_and_label_aesthetic_output_guarantees","proposal":{"problem":"A generative-art platform or commissioning institution seeks an always-terminating analyzer that accepts arbitrary artwork programs and decides whether every possible future output satisfies an explicit, machine-checkable aesthetic constraint. Testing sampled renders is liable to be mistaken for universal certification, while timeouts are liable to be reported as violations. The relevant constraint is formal—such as palette membership, compositional geometry, or absence of a specified visual pattern—not a decision about beauty itself.","actors_substrate":["generative artists and creative coders","curators and commissioning institutions","platform engineers operating artwork runtimes","viewers or exhibitors affected by incorrectly certified outputs","arbitrary generative-art programs, render parameters, and output streams","machine-checkable predicates over rendered works"],"observable_state":"The system emits a Boolean aesthetic-compliance certificate for unrestricted artwork programs even when analysis timed out, inspected only finite renders, or relied on unstated restrictions; documentation does not distinguish exact, bounded, sound-incomplete, and unknown results.","consequence":"A noncompliant output may appear after certification, or compliant works may be rejected on false alarms; engineering effort may also be spent pursuing an impossible unrestricted decider.","affected_objective":"Provide trustworthy pre-exhibition guarantees about declared formal properties without misrepresenting sampling, bounded analysis, or undecidable cases as universal aesthetic judgment.","structural_mapping":[{"archetype_element":"open-ended input class","domain_realization":"arbitrary generative-art programs with unbounded execution, interaction, or output sequences","claim_kind":"INFERENCE"},{"archetype_element":"total exact decision requirement","domain_realization":"correctly decide and terminate for every program whether all possible outputs satisfy the declared visual predicate","claim_kind":"HYPOTHESIS"},{"archetype_element":"semantic property","domain_realization":"a nontrivial property of the program's rendered behavior rather than its source syntax alone","claim_kind":"INFERENCE"},{"archetype_element":"decidable region","domain_realization":"enforceable restricted artwork languages, finite parameter spaces, or bounded render horizons","claim_kind":"INFERENCE"},{"archetype_element":"weaker honest fallback","domain_realization":"bounded exhaustive checking, sound over-approximation, or witness search returning explicit UNKNOWN","claim_kind":"INFERENCE"},{"archetype_element":"guarantee provenance","domain_realization":"a versioned certificate stating predicate, artwork-language version, bounds, assumptions, and result semantics","claim_kind":"HYPOTHESIS"}],"component_map":[{"component":"Problem-Class Specification","status":"adapted","domain_realization":"Define programs, parameter sources, interactions, output traces, and the formal visual predicate."},{"component":"Instance Representation Contract","status":"adapted","domain_realization":"Version the artwork language, renderer, asset inputs, randomness model, and predicate encoding."},{"component":"Computation Model Contract","status":"adapted","domain_realization":"State runtime powers, nondeterminism, external inputs, numeric semantics, and analyzer capabilities."},{"component":"Solvability Guarantee Profile","status":"adapted","domain_realization":"Separate universal exact decision, one-sided certification, bounded coverage, and approximation."},{"component":"Quantifier and Scope Map","status":"adapted","domain_realization":"Expose whether claims cover every program, seed, interaction, frame, and execution duration."},{"component":"Computability Status Lattice","status":"direct","domain_realization":"Classify each formulation as decidable, recognizable, partial, relative, undecidable, or unresolved."},{"component":"Constructive Procedure Witness","status":"direct","domain_realization":"For any exact fragment, retain an algorithm plus correctness and termination arguments."},{"component":"Reduction Preservation Contract","status":"direct","domain_realization":"Document the computable embedding and preserved answer if undecidability is transferred."},{"component":"Computability Impossibility Certificate","status":"adapted","domain_realization":"Retain a checked reduction for the unrestricted behavioral-certification claim."},{"component":"Assumption Register","status":"adapted","domain_realization":"Record renderer determinism, predicate decidability, input bounds, and language expressiveness."},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"List restricted artwork languages and finite regimes with enforceable membership."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"Specify which compliance or violation witnesses can be confirmed and which side remains unknown."},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"Keep UNKNOWN, timeout, out-of-scope, false, and analyzer failure distinct."},{"component":"Fallback Solution Contract","status":"adapted","domain_realization":"Label the exact bound or soundness direction of each weaker certification mode."},{"component":"Computability Guarantee Record","status":"adapted","domain_realization":"Version-link each result to artwork, model, predicate, method, assumptions, and guarantee."},{"component":"Recheck Trigger","status":"adapted","domain_realization":"Reclassify after language, renderer, predicate, plugin, or external-input changes."},{"component":"Termination Condition","status":"direct","domain_realization":"Set explicit finite budgets for bounded and semi-decision modes."},{"component":"Scope Boundary","status":"adapted","domain_realization":"Reject or quarantine programs outside the certified fragment or promise."},{"component":"Decision Record","status":"direct","domain_realization":"Record why each shipped mode and public claim was chosen."},{"component":"Uncertainty Residue","status":"direct","domain_realization":"Publish unproved obligations, abstraction imprecision, and uncovered executions."},{"component":"Independent Proof Review","status":"direct","domain_realization":"Have a separate reviewer check the theorem statement, proof, formalization, and reduction."},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"After decidability is established, assess whether certification is affordable at exhibition scale."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Over-approximate program behaviors to certify one direction while reporting false-alarm residue.","counterfactual_removal":"The proposal loses its principal sound fallback for unbounded programs."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Exhaust seeds, parameters, or traces only inside an explicit finite fence.","counterfactual_removal":"No complete bounded certification mode remains."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version the chosen boundary, guarantee, evidence, and recheck triggers.","counterfactual_removal":"The mathematics remains, but claims can drift without provenance."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Assess scaling only after a fragment is shown decidable.","counterfactual_removal":"The pilot may confuse decidability with deployability."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Required evidence before an exact fragment receives universal certification.","counterfactual_removal":"Exact positive claims would rest on tests rather than a total witness."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A direct self-referential proof is unnecessary if a simpler reduction fits the actual language.","counterfactual_removal":"No material change."},{"slug":"enumeration_and_dovetailing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Possible recognizer implementation, but bounded explicit-UNKNOWN operation is preferable for this deployment.","counterfactual_removal":"No material change."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Route each artwork to exact-fragment, sound-approximate, bounded, or escalation mode and label the result.","counterfactual_removal":"Weaker guarantees could be presented through one misleading Boolean interface."},{"slug":"halting_problem_reduction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Attempt a source-to-target embedding for unrestricted nontrivial output behavior; retain UNRESOLVED if assumptions fail.","counterfactual_removal":"There is no decisive basis for rejecting the universal decider."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Define a syntactically enforceable generative-art fragment admitting total analysis.","counterfactual_removal":"The intervention cannot recover exact guarantees for a useful governed region."},{"slug":"many_one_reduction_proof","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Supplies the total computable answer-preserving form of the impossibility transfer.","counterfactual_removal":"The reduction certificate loses explicit preservation obligations."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unenforced promises allow authoritative answers on violating inputs; enforceable syntax is safer.","counterfactual_removal":"No material change."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use one in-scope artwork to refute any overbroad analyzer claim, without treating failed search as proof.","counterfactual_removal":"The pilot loses a cheap universal-claim falsification test."},{"slug":"proof_checking","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently verify constructive and impossibility certificates and their stated theorem.","counterfactual_removal":"A subtle proof or formalization error could authorize a false boundary."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Gate the reduction on source-to-target direction, totality, computability, and named assumptions.","counterfactual_removal":"Wrong-direction hardness transfer becomes more likely."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Return witnessed YES when available and UNKNOWN at the declared budget, never infer NO from timeout.","counterfactual_removal":"Operational pressure may convert nontermination into a false verdict."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Automation of proof discovery is optional and a timeout would add another ambiguous non-result.","counterfactual_removal":"No material change."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Relative computability degrees are not needed to decide the shipped boundary.","counterfactual_removal":"No material change."}],"causal_chain":["Formalize the artwork class, renderer, aesthetic predicate, quantifiers, and computation model.","Seek both a total constructive analyzer for restricted classes and a valid impossibility reduction for the unrestricted behavioral claim.","Enforce decidable syntax or finite bounds where exact termination is provable.","For remaining inputs, route to sound abstraction or bounded witness search with explicit UNKNOWN.","Attach the precise guarantee and assumptions to every result, preventing samples or timeouts from becoming universal certificates.","Recheck the boundary when the artwork language, renderer, predicate, or external capabilities change."],"baseline":"Render a finite sample of seeds or frames, apply a visual rule, and report pass/fail; retry or time out on difficult programs, with curators informally reviewing exceptions.","nearest_rival":"A larger randomized testing and human-review pipeline that improves empirical coverage but still cannot justify a class-wide guarantee.","authority_safety":{"affected_parties":["artists whose works may be accepted, rejected, or constrained","curators and platform operators relying on certificates","viewers or exhibitors exposed to uncaught outputs"],"decision_authority":"The institution operating the analyzer may define its accepted artwork language and labels; artists retain authority over whether to submit to the restricted certification regime, and curators retain final exhibition judgment.","authorized_first_step":"On a sandboxed corpus of 20 consenting test artworks, formalize one decidable frame predicate and compare sampled testing with bounded exhaustive analysis on finite seed and 100-frame traces; issue only BOUNDED_PASS, COUNTEREXAMPLE, UNKNOWN, or OUT_OF_SCOPE.","excluded_actions":["claiming to decide beauty, artistic merit, or audience response","executing untrusted artwork outside a sandbox","silently rejecting out-of-fragment works","using UNKNOWN or timeout as evidence of violation","generalizing bounded results beyond their declared horizon"],"halt_rollback":"Stop the pilot and withdraw its certificates if an allegedly exhaustive case was omitted, a sound abstraction misses a concrete behavior, labels are consumed as universal judgments, or proof review finds a scope mismatch; preserve logs and revert affected results to UNKNOWN pending reclassification."}},"negative_tests":{"strongest_counterevidence":"The deployed artwork language may already be finite-state or syntactically terminating, making the target property decidable; alternatively, the desired judgment may actually be subjective beauty rather than a stable machine predicate, in which case ontology—not computability—is the primary problem.","analogy_break":"Unlike arbitrary program semantics, many visual properties of a single completed finite image are directly decidable. The impossibility argument applies only when the claim quantifies over unrestricted program behavior or unbounded possible outputs.","failure_condition":"The mapping fails if stakeholders cannot state a stable output predicate, if only individual completed works require evaluation, or if no reusable universal guarantee is claimed.","problem_falsifier":"Inventory shows every accepted artwork has a finite, effectively enumerable state space and the requested predicate is decidable on every enumerated output, with no unrestricted or unbounded claim.","intervention_falsifier":"Under the stated model, independent review finds the reduction invalid and a total correct analyzer exists for the full declared class, or the fallback labels do not reduce false universal interpretations relative to baseline.","risks":["Formal constraints may be mistaken for aesthetic value judgments.","Restricted languages may suppress artistically important expressiveness.","Coarse abstraction may generate exclusionary false alarms.","Bounds may be selected to certify typical demos while missing realistic long-running behavior.","Institutional labels may acquire authority beyond their formal scope."]},"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 transfer. The candidate deliberately targets formal properties of unbounded generative behavior, not subjective aesthetic merit; applicability depends on the actual language and quantifiers."}