{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__information_theory","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"information_theory","decision":"CANDIDATE","problem_id":"universal_shortest_description_decision_overclaim","causal_lever_id":"model_relative_compressibility_boundary_routing","proposal":{"problem":"An information system is required to determine, for every finite string, whether a shorter generating description exists or to return a provably shortest description. Heuristic search success and timeouts are then presented as exact compressibility or incompressibility verdicts.","actors_substrate":["compression or algorithmic-information researchers","compression-service engineers","downstream users interpreting scores","independent proof reviewers","finite strings, programs, and a fixed decoding machine"],"observable_state":"The interface emits unconditional shortest-description or incompressible labels for arbitrary strings, despite relying on time-bounded program search and lacking a class-wide termination proof.","consequence":"Some strings receive unsupported optimality or incompressibility claims; continued engineering cannot make the unrestricted exact procedure total, while silent changes to the decoder change the claimed quantity.","affected_objective":"Provide useful compression evidence without misrepresenting model-relative, one-sided, or bounded results as universal exact decisions.","structural_mapping":[{"archetype_element":"Open-ended class requiring exact terminating answers","domain_realization":"All finite strings and thresholds under a fixed universal decoder, with exact shortest-description guarantees.","claim_kind":"INFERENCE"},{"archetype_element":"Implicit representation and computation model","domain_realization":"Description language, decoder, machine encoding, and any oracle or resource bound determine the compressibility question.","claim_kind":"CORPUS"},{"archetype_element":"Universal impossibility boundary","domain_realization":"Exact shortest-program length for arbitrary strings cannot be supplied by a total effective procedure under the stated unrestricted model.","claim_kind":"INFERENCE"},{"archetype_element":"One-sided evidence","domain_realization":"Dovetailed program execution can eventually witness that a description shorter than a threshold exists, but failure to find one cannot certify incompressibility.","claim_kind":"INFERENCE"},{"archetype_element":"Restricted decidable region","domain_realization":"Finite description and execution bounds make exhaustive checking total, with conclusions explicitly limited to those bounds.","claim_kind":"INFERENCE"},{"archetype_element":"Governed fallback","domain_realization":"Queries are routed to witnessed YES, bounded UNKNOWN, or ordinary heuristic-compression modes with distinct labels.","claim_kind":"HYPOTHESIS"}],"component_map":[{"component":"Problem-Class Specification","status":"direct","domain_realization":"Decide K_U(x)<k or return a shortest U-program for arbitrary finite x."},{"component":"Instance Representation Contract","status":"direct","domain_realization":"Fix U, program encoding, string encoding, and threshold convention."},{"component":"Computation Model Contract","status":"direct","domain_realization":"Ordinary effective computation without a halting oracle; declare all bounds."},{"component":"Solvability Guarantee Profile","status":"direct","domain_realization":"Separate total exact decision, recognition, bounded decision, and heuristic evidence."},{"component":"Quantifier and Scope Map","status":"direct","domain_realization":"Distinguish every x and k from tested samples or bounded subsets."},{"component":"Computability Status Lattice","status":"adapted","domain_realization":"Unrestricted exact: unavailable; shorter-witness side: recognizable; bounded variant: decidable."},{"component":"Constructive Procedure Witness","status":"adapted","domain_realization":"Dovetailed witness search and finite bounded enumeration."},{"component":"Reduction Preservation Contract","status":"omitted","domain_realization":"No reduction is needed if the direct diagonal certificate is used."},{"component":"Computability Impossibility Certificate","status":"direct","domain_realization":"Checked diagonal argument for the fixed-machine unrestricted claim."},{"component":"Assumption Register","status":"direct","domain_realization":"Record decoder universality, effectiveness, encodings, quantifiers, and oracle exclusions."},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"Map finite program-length/runtime bounds and enforceable restricted description languages."},{"component":"One-Sided Recognition Contract","status":"direct","domain_realization":"A found shorter program supports YES; no elapsed time supports NO."},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"Budget exhaustion returns UNKNOWN, distinct from incompressible and failure."},{"component":"Fallback Solution Contract","status":"direct","domain_realization":"Publish heuristic compression length or bounded evidence without shortest-description claims."},{"component":"Computability Guarantee Record","status":"direct","domain_realization":"Version the model, proof, bounds, output semantics, and shipped claim."},{"component":"Recheck Trigger","status":"direct","domain_realization":"Reclassify after decoder, language, oracle, bound, or guarantee changes."},{"component":"Termination Condition","status":"adapted","domain_realization":"Apply explicit step, time, description-length, and enumeration bounds to total fallbacks."},{"component":"Scope Boundary","status":"direct","domain_realization":"Unrestricted strings are not covered by exact negative verdicts."},{"component":"Decision Record","status":"direct","domain_realization":"Record the selected interface tier and why stronger claims were rejected."},{"component":"Uncertainty Residue","status":"direct","domain_realization":"Retain UNKNOWN plus uncertainty about formalization fidelity and practical coverage."},{"component":"Independent Proof Review","status":"direct","domain_realization":"A separate reviewer checks the exact theorem and assumptions."},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"Analyze cost only after a bounded or restricted variant is shown decidable."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No natural safety-property abstraction preserves shortest-description claims.","counterfactual_removal":"No causal change."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Enumerate programs only within explicit length and execution bounds.","counterfactual_removal":"The bounded total fallback disappears."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version the model, verdict, interface labels, and triggers.","counterfactual_removal":"Guarantees can drift silently."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Assess bounded-search feasibility after decidability classification.","counterfactual_removal":"The pilot could select an unusable bound."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Prove totality and correctness only for restricted fallbacks.","counterfactual_removal":"Fallback guarantees lack a positive witness."},{"slug":"diagonalization_impossibility_proof","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Apply directly to the fixed-decoder universal exact claim.","counterfactual_removal":"The boundary rests on failed search rather than proof."},{"slug":"enumeration_and_dovetailing","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Fairly search candidate programs for shorter-description witnesses.","counterfactual_removal":"Complete YES-side recognition is lost."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Route to exact bounded, witness, heuristic, or UNKNOWN modes.","counterfactual_removal":"Weaker evidence can be mistaken for exact judgment."},{"slug":"halting_problem_reduction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A possible alternative certificate, unnecessary beside direct diagonalization.","counterfactual_removal":"No change to the chosen proof path."},{"slug":"language_fragment_restriction","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Use mechanically enforceable restricted description languages where a decider exists.","counterfactual_removal":"One useful decidable region is unavailable."},{"slug":"many_one_reduction_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No transfer proof is selected.","counterfactual_removal":"No change."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unchecked promises risk authoritative answers outside their guarantee; enforceable fragments are clearer.","counterfactual_removal":"No change."},{"slug":"proof_by_counterexample","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Refutes implementations, not existence of every possible decider.","counterfactual_removal":"No boundary evidence is lost."},{"slug":"proof_checking","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently verify the diagonal proof and bounded-fallback proofs.","counterfactual_removal":"A formalization or inference gap can authorize a false boundary."},{"slug":"reduction_direction_checklist","disposition":"unused","contribution_type":"NONE","adaptation_or_rejection":"No reduction is selected.","counterfactual_removal":"No change."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Stop witness search at a declared budget and emit UNKNOWN, never NO.","counterfactual_removal":"Timeouts can become false incompressibility verdicts."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Optional implementation aid, not required for the first classification.","counterfactual_removal":"The causal chain remains intact."},{"slug":"turing_reduction_analysis","disposition":"unused","contribution_type":"NONE","adaptation_or_rejection":"Relative degrees do not improve the proposed user-facing boundary.","counterfactual_removal":"No change."}],"causal_chain":["Fix the decoder, representation, computation model, quantifiers, and requested guarantee.","Independently check a diagonal impossibility certificate for unrestricted exact shortest-description decisions.","Classify shorter-description discovery as one-sided recognition and bounded variants as decidable.","Route each query to the strongest applicable mode while preserving UNKNOWN and model-relative labels.","Prevent timeout and best-so-far results from becoming exact incompressibility claims."],"baseline":"Run practical compressors or program search to a timeout; report the shortest result found and sometimes treat failure as evidence of incompressibility.","nearest_rival":"Benchmark several heuristic compressors and report the best achieved length with no computability classification; useful empirically but unable to certify global optimality.","authority_safety":{"affected_parties":["users relying on compressibility labels","engineers operating the search service","researchers whose results are compared","downstream automated decision systems"],"decision_authority":"The product owner may authorize a bounded labeling pilot; changing the mathematical boundary requires an independently reviewed proof and specification owner approval.","authorized_first_step":"On a finite synthetic corpus, prototype fixed-model outputs YES-with-witness, UNKNOWN-at-budget, and bounded-exact; audit that no interface or log converts UNKNOWN into NO.","excluded_actions":["claiming universal incompressibility from timeout","silently changing the decoder or bounds","deploying exact-negative labels to consequential decisions","treating human judgment as an undeclared oracle"],"halt_rollback":"Halt if the proof review finds a model mismatch, any UNKNOWN is rendered as NO, or bounded claims escape their scope; disable exact-negative labels and revert to explicitly heuristic lengths."}},"negative_tests":{"strongest_counterevidence":"The operational requirement may actually concern expected code length for an explicit computable source distribution, or a finite catalog with bounded decoding; then a known total procedure may exist and the issue is complexity, not computability.","analogy_break":"Shannon entropy and practical compression performance concern distributions or achieved codes; they do not by themselves establish the uncomputability or value of an individual string's exact shortest program.","failure_condition":"The proposal fails if fixed-model distinctions cannot be exposed to callers, restricted membership cannot be enforced, or UNKNOWN is operationally treated as a negative answer.","problem_falsifier":"Show that the real requirement is confined to an effectively finite, enforceable class or asks only for achieved/expected compression rather than universally exact shortest descriptions.","intervention_falsifier":"In the bounded pilot, the routed interface does not reduce unsupported exact claims, produces unusably many UNKNOWN results without decision value, or independent review cannot validate the stated boundary.","risks":["Users may interpret model-relative scores as intrinsic properties.","Bounds may be chosen to make the fallback vacuously safe.","A checked theorem may formalize the wrong decoder or requirement.","Restricted languages may omit practically important structure.","Heuristic outputs may regain exact-sounding labels downstream."]},"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":0.91,"generator_notes":"Closed-book inference from the supplied packet. The candidate targets exact individual-description optimality, not ordinary source coding or compression engineering."}