{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"deadweight_loss_reduction__mathematics","trajectory_id":"R","attempt_index":0,"archetype_slug":"deadweight_loss_reduction","domain_slug":"mathematics","decision":"CANDIDATE","problem_id":"overstrong_theorem_hypotheses_block_valid_applications","causal_lever_id":"assumption_minimization_with_counterexample_boundaries","proposal":{"problem":"A theorem has sufficient but unnecessarily strong hypotheses, excluding mathematical objects for which its conclusion remains true. The excess assumptions form an avoidable applicability wedge, while assumptions necessary for truth must remain protected.","actors_substrate":["theorem authors","downstream mathematicians","formal-library maintainers","mathematical objects satisfying some but not all stated hypotheses","the theorem's hypotheses, proof, conclusion, and counterexamples"],"observable_state":"Researchers repeatedly prove bespoke variants for excluded cases, cannot reuse the theorem on boundary objects, or retain assumptions used only for proof convenience; HYPOTHESIS: such patterns occur in the selected theorem family.","consequence":"Sound conclusions remain unavailable across part of their valid domain, duplicating proof effort and fragmenting theory.","affected_objective":"Maximize sound theorem applicability and reusable proof value without admitting any false instance.","structural_mapping":[{"archetype_element":"value-blocking wedge","domain_realization":"An overstrong hypothesis excludes objects from the theorem's admissible domain even when the conclusion is true.","claim_kind":"INFERENCE"},{"archetype_element":"beneficial activity blocked","domain_realization":"Sound application and reuse of the theorem on excluded cases.","claim_kind":"INFERENCE"},{"archetype_element":"protected purpose","domain_realization":"Logical validity: every admitted object must satisfy the conclusion, with explicit dependencies and no hidden assumptions.","claim_kind":"CORPUS"},{"archetype_element":"redesign lever","domain_realization":"Remove or weaken candidate hypotheses individually, reconstruct the proof, and locate necessity with counterexamples.","claim_kind":"HYPOTHESIS"},{"archetype_element":"incidence and behavioral response","domain_realization":"Generalization benefits downstream users but may increase proof complexity, maintenance burden, or misuse risk.","claim_kind":"HYPOTHESIS"},{"archetype_element":"bounded reversible implementation","domain_realization":"Pilot one theorem family while retaining the original theorem as a proved corollary.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Distortion Map","status":"direct","domain_realization":"Trace each stated hypothesis to proof steps and excluded object classes."},{"component":"Protected Constraint Safeguard","status":"direct","domain_realization":"Require a complete proof for the weakened statement and counterexample checks at its boundary."},{"component":"Surplus Estimate","status":"adapted","domain_realization":"Estimate added admissible cases, reusable downstream results, and avoided duplicate lemmas; do not monetize them."},{"component":"Affected-Party Incidence Map","status":"adapted","domain_realization":"Record benefits and burdens for authors, users, and library maintainers."},{"component":"Redesign Lever","status":"direct","domain_realization":"Delete, weaken, or replace nonessential hypotheses."},{"component":"Distributional Review","status":"adapted","domain_realization":"Check whether broader applicability shifts disproportionate proof or maintenance costs to reviewers and maintainers."},{"component":"Behavioral Response Model","status":"adapted","domain_realization":"Anticipate overapplication, preference for simpler strong corollaries, and proliferation of variants."},{"component":"Implementation Boundary","status":"direct","domain_realization":"Limit the pilot to one theorem family and predefined hypothesis changes."},{"component":"Monitoring and Rebound Check","status":"adapted","domain_realization":"Track proof failures, misuse, duplicated variants, downstream reuse, and maintenance cost."},{"component":"Rollback or Adjustment Rule","status":"direct","domain_realization":"Retain the original theorem and revert the generalized interface if soundness or usability gates fail."},{"component":"Cost–Benefit Assessment Frame","status":"adapted","domain_realization":"Compare increased applicability with proof complexity, review effort, and maintenance burden."},{"component":"Price-Wedge Diagnostic","status":"incompatible","domain_realization":"No monetary or scarcity price controls theorem applicability."},{"component":"Friction Source Breakdown","status":"direct","domain_realization":"Separate logically necessary assumptions from proof convenience, notation, tooling, and library-policy friction."},{"component":"Compensating Adjustment Plan","status":"adapted","domain_realization":"Preserve the original stronger statement as an easy-to-use corollary and document migration."},{"component":"Legitimacy and Authority Review","status":"adapted","domain_realization":"Authors or authorized maintainers approve statement and library changes; proof validity remains non-negotiable."},{"component":"Sensitivity Analysis","status":"adapted","domain_realization":"Test alternative weakenings and identify which assumptions change truth, proof length, or tractability."},{"component":"Pilot or Sunset Path","status":"adapted","domain_realization":"Run a bounded generalization pilot with an expiry decision for the new interface, not for mathematical truth."}],"mechanism_dispositions":[{"slug":"congestion_or_capacity_pricing_adjustment","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"There is no time-varying access price or congestible capacity.","counterfactual_removal":"No change."},{"slug":"cost_benefit_assessment_protocol","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Replace monetary welfare with applicability, reuse, proof complexity, and maintenance measures.","counterfactual_removal":"The pilot could generalize a theorem whose added reach does not justify its complexity."},{"slug":"distortion_reduction_review","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Audit hypothesis necessity while separating avoidable restrictions from truth-preserving conditions.","counterfactual_removal":"There would be no disciplined basis for identifying the removable assumption."},{"slug":"impact_assessment_table","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Tabulate effects on users, authors, and maintainers plus monitoring triggers.","counterfactual_removal":"Incidence and maintenance burdens become easier to overlook."},{"slug":"matching_improvement_program","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The binding failure is theorem admissibility, not pairing willing parties.","counterfactual_removal":"No change."},{"slug":"permit_or_approval_streamlining","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Review delay may exist but is not the proposed causal wedge.","counterfactual_removal":"The hypothesis-minimization chain remains intact."},{"slug":"price_control_redesign","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"No administered price protects theorem soundness.","counterfactual_removal":"No change."},{"slug":"quota_or_allocation_rule_review","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Adapt eligibility review to distinguish the valid domain boundary from a stale sufficient-condition boundary.","counterfactual_removal":"The intervention loses its explicit test of whether excluded cases can be admitted safely."},{"slug":"regulatory_simplification_pilot","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Pilot weakened hypotheses on one theorem family while retaining the original result.","counterfactual_removal":"Failure exposure and reversal costs increase."},{"slug":"sunset_clause_review","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Established mathematical truth does not expire; only the pilot interface needs a decision date.","counterfactual_removal":"No material causal change."},{"slug":"tariff_fee_or_toll_redesign","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"No authority-imposed charge creates the exclusion.","counterfactual_removal":"No change."}],"causal_chain":["Audit one theorem's hypotheses and proof dependencies.","Identify a candidate assumption not required by known counterexamples or the protected conclusion.","Formulate a precise weakened statement and reconstruct a proof or derive the exact boundary where proof fails.","Publish the generalized theorem beside the original as a corollary during a bounded library pilot.","Eligible sound applications expand, reducing bespoke variants and duplicated proof effort.","Monitor reuse, misuse, proof complexity, and maintenance burden; retain, narrow, or roll back the interface."],"baseline":"Keep the established theorem unchanged and handle excluded cases through bespoke proofs or separate stronger-context corollaries.","nearest_rival":"Prove an isolated alternative theorem for one excluded class without systematically testing which original assumptions are necessary.","authority_safety":{"affected_parties":["theorem authors","downstream users","reviewers","formal-library maintainers"],"decision_authority":"The theorem author or repository maintainer may authorize the pilot; mathematical validity is determined only by an accepted proof under the system's rules.","authorized_first_step":"Select one theorem with at most four substantive hypotheses; audit one hypothesis, attempt one weakened proof, search the bounded object class for counterexamples, and stage the result without replacing the original theorem.","excluded_actions":["Treating failed counterexample search as proof","Weakening multiple hypotheses without isolating effects","Removing soundness checks","Deleting or silently changing the original theorem","Claiming measured downstream demand without evidence"],"halt_rollback":"Halt if a counterexample is found, the proof cannot be completed, hidden dependencies appear, or review cost exceeds the preset budget; withdraw the staged generalization and retain the original theorem."}},"negative_tests":{"strongest_counterevidence":"A necessity proof or counterexample shows every targeted hypothesis is required, or excluded cases contribute no reusable applications while generalization materially increases complexity.","analogy_break":"Mathematics has no literal exchange surplus or price-mediated actors; applicability and avoided proof duplication are only proxies for value, and truth cannot be traded against aggregate benefit.","failure_condition":"The method repeatedly selects hypotheses that are necessary, creates unusable statements, or shifts more work to proof maintenance than it avoids.","problem_falsifier":"The theorem's hypotheses are already minimal over the stated domain, or no excluded object satisfies the conclusion.","intervention_falsifier":"Within the bounded pilot, no candidate weakening yields both a valid proof and at least one independently useful new application, or the generalized interface breaches the preset complexity or maintenance threshold.","risks":["Unsound generalization from incomplete counterexample search","Proof complexity obscuring the result","Users overapplying a more technical theorem","Metric gaming through trivial added cases","Maintenance burden shifted to library stewards","Credit disputes with authors of earlier special cases"]},"null_rationale":null,"classification":{"candidate_kind":"MECHANISM_ADAPTATION","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":0.83,"generator_notes":"Closed-book structural transfer. The candidate treats unnecessary sufficient conditions as an applicability wedge while preserving proof validity as the protected constraint; empirical prevalence and benefits remain hypotheses."}