{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__operations_research","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"operations_research","decision":"CANDIDATE","problem_id":"universal_executable_constraint_optimizer_overclaim","causal_lever_id":"enforced_solvable_input_classes_and_labeled_fallbacks","proposal":{"problem":"An operations-research service accepts arbitrary executable constraint, transition, or objective callbacks yet promises an exact feasible/optimal answer with guaranteed termination for every submitted planning model. Some jobs hang or time out and are reported as infeasible, although the unrestricted input language may encode nontermination; the service therefore conflates undecidability, computational difficulty, and infeasibility.","actors_substrate":["OR platform owners and solver engineers","model authors and planners","downstream systems consuming schedules or infeasibility verdicts","executable model language, solver runtime, and audit records"],"observable_state":"Models outside a proved-total fragment enter the exact-solver path; runtimes can diverge; timeout, infeasible, unknown, and out-of-scope states are collapsed; documentation retains a universal exactness claim.","consequence":"Resources are spent pursuing an impossible universal solver, while valid plans may be rejected and unsupported outputs may drive operational decisions.","affected_objective":"Truthful, terminating, and practically useful optimization decisions across the declared model class.","structural_mapping":[{"archetype_element":"unrestricted formal problem class","domain_realization":"planning models containing arbitrary executable callbacks","claim_kind":"HYPOTHESIS"},{"archetype_element":"universal exact terminating guarantee","domain_realization":"return an optimum or valid infeasibility verdict for every accepted model","claim_kind":"INFERENCE"},{"archetype_element":"computability boundary","domain_realization":"boundary between enforceable finite/decidable optimization languages and callbacks capable of unbounded computation","claim_kind":"HYPOTHESIS"},{"archetype_element":"honest weaker fallback","domain_realization":"exact restricted solving, bounded search, one-sided witness search, or UNKNOWN with explicit labels","claim_kind":"INFERENCE"}],"component_map":[{"component":"Problem-Class Specification","status":"direct","domain_realization":"Define the accepted planning-model class and decision question."},{"component":"Instance Representation Contract","status":"direct","domain_realization":"Version grammar, data domains, horizons, and callback semantics."},{"component":"Computation Model Contract","status":"direct","domain_realization":"Declare solver machine, callback powers, external services, and resource accounting."},{"component":"Solvability Guarantee Profile","status":"direct","domain_realization":"Separate exact-total, one-sided, bounded, and approximate guarantees."},{"component":"Quantifier and Scope Map","status":"direct","domain_realization":"Identify whether claims cover every model, a fragment, or bounded instances."},{"component":"Computability Status Lattice","status":"adapted","domain_realization":"Classify model families as decidable, recognizable, relative, unresolved, or undecidable."},{"component":"Constructive Procedure Witness","status":"direct","domain_realization":"Provide an algorithm plus correctness and termination arguments for each exact fragment."},{"component":"Reduction Preservation Contract","status":"direct","domain_realization":"Require a computable semantics-preserving encoding for any hardness transfer."},{"component":"Computability Impossibility Certificate","status":"direct","domain_realization":"Retain the checked reduction or direct proof against unrestricted exact solving."},{"component":"Assumption Register","status":"direct","domain_realization":"Record finiteness, callback totality, numeric semantics, and oracle assumptions."},{"component":"Decidable Subclass Map","status":"direct","domain_realization":"Map enforceable LP/MILP, finite-state, bounded-horizon, or other proved fragments."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"Permit verified feasible-plan witnesses without claiming exhaustive infeasibility."},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"Keep UNKNOWN, timeout, out-of-scope, failure, and infeasible distinct."},{"component":"Fallback Solution Contract","status":"direct","domain_realization":"Specify routing, guarantees, budgets, and labels for weaker modes."},{"component":"Computability Guarantee Record","status":"direct","domain_realization":"Version-link shipped claims to proofs, model language, and solver."},{"component":"Recheck Trigger","status":"direct","domain_realization":"Reclassify after language, callback, oracle, or guarantee changes."},{"component":"Termination Condition","status":"direct","domain_realization":"Give proof-based termination for exact fragments and budgets for fallbacks."},{"component":"Scope Boundary","status":"direct","domain_realization":"Mechanically reject or quarantine models outside supported fragments."},{"component":"Decision Record","status":"direct","domain_realization":"Record the chosen boundary and operational rationale."},{"component":"Uncertainty Residue","status":"direct","domain_realization":"List unproved reductions, termination obligations, and semantic mismatches."},{"component":"Independent Proof Review","status":"direct","domain_realization":"Have an independent reviewer check formalization, reductions, and termination."},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"Send decidable fragments to scaling and architecture analysis."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Use finite over-approximations for safety constraints, with one-directional labels.","counterfactual_removal":"Fallback precision decreases, but the boundary remains viable."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Exhaustively test small horizons and finite domains without extrapolation.","counterfactual_removal":"The pilot loses a complete bounded check."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version the boundary, guarantee, evidence, and recheck triggers.","counterfactual_removal":"Guarantees can drift silently."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Assess tractability only after decidability classification.","counterfactual_removal":"Decidable but impractical fragments may be shipped."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Require totality and correctness witnesses for exact solver modes.","counterfactual_removal":"Exact-total labels lack positive evidence."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A direct self-reference proof is unnecessary if a valid reduction suffices.","counterfactual_removal":"No change unless reduction proof fails."},{"slug":"enumeration_and_dovetailing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Generic dovetailing is less operationally suitable than bounded witness search.","counterfactual_removal":"No material change."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Route by enforceable class to exact, bounded, sound-approximate, or escalation modes.","counterfactual_removal":"Unsupported models again reach an overclaimed exact path."},{"slug":"halting_problem_reduction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Attempt a checked reduction through executable callbacks before declaring undecidability.","counterfactual_removal":"The impossibility claim remains conjectural."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Enforce a syntactic, decidable modeling fragment at ingestion.","counterfactual_removal":"No enforceable exact-total service boundary exists."},{"slug":"many_one_reduction_proof","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Use as the formal preservation contract for the halting reduction.","counterfactual_removal":"Hardness transfer is less auditable."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unenforced semantic promises permit authoritative wrong answers; prefer checked syntax.","counterfactual_removal":"No loss under syntactic enforcement."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use one in-scope divergent callback to refute an existing universal implementation claim, not prove undecidability.","counterfactual_removal":"Overclaim refutation may take longer."},{"slug":"proof_checking","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently check formalization, totality, and impossibility evidence.","counterfactual_removal":"A flawed proof could hard-gate legitimate models."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Gate the source-to-target reduction and expose assumptions.","counterfactual_removal":"Direction errors become likelier."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Return verified FEASIBLE or budgeted UNKNOWN, never infer INFEASIBLE from timeout.","counterfactual_removal":"Timeouts can again become false negatives."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Optional proof discovery adds no necessary guarantee beyond independent certificate checking.","counterfactual_removal":"Manual proof production remains possible."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Relative oracle degrees do not answer the immediate deployable-boundary question.","counterfactual_removal":"No material change."}],"causal_chain":["Executable model language permits unbounded computation.","A universal optimizer must resolve feasibility or optimality for every such model and terminate.","A valid reduction would show that this guarantee decides whether embedded computation halts.","The unrestricted exact-total claim is withdrawn if that proof passes independent review.","An enforceable decidable fragment admits constructive exact solvers; other inputs receive labeled weaker modes or rejection.","Distinct UNKNOWN and timeout states prevent unsupported infeasibility decisions."],"baseline":"Accept all syntactically valid models, run the exact solver until a timeout, and translate exhaustion into infeasible or failure.","nearest_rival":"Keep the unrestricted language and improve solver heuristics, limits, and compute capacity without classifying solvability.","authority_safety":{"affected_parties":["model authors","planners and operators","people subject to allocation or scheduling decisions","solver and platform teams"],"decision_authority":"Platform owner may change claims and routing; model owners approve fragment migration; operational decision owners approve use of weaker outputs.","authorized_first_step":"Offline, sample one model family, formalize callback semantics, attempt and independently review a halting reduction, then compare current versus restricted routing on bounded fixtures; do not alter production decisions.","excluded_actions":["Do not label timeout as infeasible.","Do not generalize bounded results beyond their bound.","Do not block production model classes solely on an unchecked analogy.","Do not let approximate or one-sided outputs trigger irreversible allocation automatically."],"halt_rollback":"Stop the pilot if formal semantics do not represent deployed callbacks, review finds a proof gap, or fixtures show status-label corruption; retain existing production routing and mark the classification unresolved."}},"negative_tests":{"strongest_counterevidence":"The deployed language may be a finite, effectively enumerable LP/MILP or bounded-state grammar with no unbounded callbacks; then total solving is computable and the real issue is complexity.","analogy_break":"Optimization adds an objective and feasibility structure; undecidability transfers only if the actual encoding can faithfully simulate unbounded computation. Finite horizons, bounded variables, or forced-total callbacks break the halting analogy.","failure_condition":"The restriction excludes most operational models, membership is not enforceable, or downstream systems still collapse UNKNOWN into infeasible.","problem_falsifier":"Audit shows every accepted model belongs to a proved decidable class and no universal guarantee is made outside it; observed failures are exclusively resource scaling.","intervention_falsifier":"Independent review cannot validate either a constructive total solver for the proposed fragment or the claimed reduction for the unrestricted class, or labeled routing fails to reduce false infeasibility without unacceptable coverage loss.","risks":["Overrestricting expressiveness","Enshrining a proof about the wrong semantics","UNKNOWN outputs being ignored or coerced","Confusing decidability with tractability","Adversarial models evading fragment checks"]},"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":0.86,"generator_notes":"Closed-book inference. The target is conditional on executable callbacks having enough expressiveness to encode unbounded computation; that premise and the reduction require verification."}