{"schema_version":1,"assessment_id":"eoa_inverse_innovation_exp03_opportunity320_20260801","source_experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"deadweight_loss_reduction__mathematics","archetype_slug":"deadweight_loss_reduction","domain_slug":"mathematics","title":"Bounded minimization of overstrong theorem hypotheses","opportunity_summary":"Audit one theorem with at most four substantive hypotheses, isolate one potentially unnecessary assumption, and attempt a proved weakening with counterexample boundaries. The proposal could expand sound applicability and reduce bespoke proofs, but no theorem instance, useful excluded application, downstream demand, or prior-art position is established.","adopter_authorizer":"A theorem author or formal-library repository maintainer can authorize a staged pilot; acceptance of the proof under the relevant mathematical or formal system determines validity.","scores":{"meaningful_impact":{"score":3,"rationale":"A successful weakening could make one conclusion soundly reusable for excluded objects and avoid bespoke variants, but the packet identifies no concrete theorem, affected applications, or measured duplication."},"stakeholder_pull":{"score":2,"rationale":"Theorem authors, downstream mathematicians, and library maintainers are identifiable beneficiaries, but repeated demand and willingness to review or maintain a generalized theorem remain explicit hypotheses."},"incremental_advantage":{"score":4,"rationale":"Compared with leaving the theorem unchanged or proving one isolated alternative, auditing a single hypothesis can expose a broader validity boundary and produce a reusable general theorem; whether that advantage materializes is testable in the proposed pilot."},"distinctiveness_plausibility":{"score":2,"rationale":"The systematic combination of proof reconstruction, bounded counterexample search, and rollback is coherent, but the packet marks prior art as unsearched and supplies no basis for distinguishing it from established theorem-generalization or library-refactoring practice."},"technical_implementability":{"score":4,"rationale":"The first step is technically bounded to one theorem and one hypothesis, with proof acceptance and counterexamples providing decisive tests. Implementability is reduced by the absence of a named theorem and the possibility of hidden proof dependencies."},"adoption_authority_feasibility":{"score":4,"rationale":"The theorem author or repository maintainer has a defined authorization role, the result can be staged beside the original, and validity remains subject to accepted proof. Actual maintainer participation is not established."},"evidence_readiness":{"score":3,"rationale":"The candidate provides separate problem and intervention falsifiers, a bounded audit, and halt conditions, but lacks a selected theorem family, admissible object class, usefulness criterion, and precommitted complexity threshold."},"safety_net_benefit":{"score":5,"rationale":"The original theorem is retained, failed counterexample search is not treated as proof, validity checks remain mandatory, and the staged generalization can be withdrawn if proof, dependency, complexity, or review conditions fail."},"scalability":{"score":3,"rationale":"The audit procedure could be repeated across theorem families, but each weakening requires theorem-specific proof work, counterexample analysis, review, and maintenance, with no evidence yet that reusable gains exceed those recurring burdens."}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Select one theorem, define the bounded object class and thresholds, audit one hypothesis, attempt the weakened proof, perform bounded counterexample analysis, and obtain an independent mathematical review.","confidence":"LOW","assumptions":["One theorem has at most four substantive hypotheses.","A qualified mathematician or formalizer and one reviewer can complete the bounded attempt within several person-weeks.","No unusually expensive proprietary data, hardware, or compliance process is required.","The estimate includes failed proof effort within the preset pilot boundary."]},"initial_deployment_startup":{"band_2026_usd":"10K_TO_50K","scope":"Formalize or package one proved generalization, stage it beside the original theorem, add documentation and tests, and complete repository review without replacing the existing interface.","confidence":"LOW","assumptions":["The weakened proof succeeds during the evidence phase.","The target repository already has suitable tooling and contributor processes.","Only one theorem and its immediate documentation or dependency tests are changed.","No extensive downstream migration is undertaken."]},"operational_launch":{"band_2026_usd":"10K_TO_50K","scope":"Publish the accepted generalization, document applicability boundaries and misuse risks, demonstrate at least one independent new application, and monitor the bounded pilot through its retain-or-withdraw decision.","confidence":"LOW","assumptions":["The theorem author or maintainer agrees to participate.","Review and integration do not uncover broad hidden dependencies.","The original theorem remains available as a corollary or stable interface.","Monitoring is limited to one library or theorem community."]},"annual_recurring":{"band_2026_usd":"UNDER_10K","scope":"Maintain the added theorem and documentation, address occasional user questions or breakages, and review evidence of reuse, misuse, and proof-maintenance burden for one accepted generalization.","confidence":"LOW","assumptions":["Only one generalized theorem is maintained.","The proof is stable under normal library evolution.","No recurring large-scale counterexample campaign or downstream migration is required.","Scaling the method to additional theorems would require separate project costs."]}},"research_burden":"HIGH","earliest_credible_horizon":"3_TO_12_MONTHS","pipeline_gates":{"recognizable_externally_supportable_problem":{"status":"YES","reason":"The sealed candidate specifies the recognizable problem of sufficient but unnecessarily strong theorem hypotheses, observable through excluded boundary objects, bespoke variants, or assumptions used only for proof convenience, while allowing minimality to falsify the problem."},"identifiable_adopter_or_authorizer":{"status":"YES","reason":"The theorem author or repository maintainer is explicitly identified as pilot authorizer, with proof acceptance under the governing system retaining authority over mathematical validity."},"distinct_testable_incremental_claim":{"status":"YES","reason":"The proposal claims that systematic removal of one unnecessary hypothesis can yield a proved, reusable statement beyond both the unchanged theorem and an isolated alternative; a counterexample, failed proof, absent useful application, or excessive complexity can refute that claim."},"bounded_next_evidence_step":{"status":"YES","reason":"The packet limits the first step to one theorem with at most four hypotheses, one audited assumption, one weakened proof attempt, a bounded counterexample search, independent review, and staging without replacing the original."},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"Soundness is non-negotiable, failed search cannot substitute for proof, the original theorem is retained, and explicit halt and withdrawal conditions address counterexamples, hidden dependencies, proof failure, and excessive review cost."},"implementation_cost_scope_and_range":{"status":"UNCERTAIN","reason":"The one-theorem scope is bounded, but no theorem family, proof environment, object-class size, review budget, or complexity threshold is supplied, so the broad cost bands remain assumption-driven rather than candidate-verified."}},"blocking_evidence":["A concrete theorem instance with one plausibly unnecessary hypothesis and at least one excluded object for which the conclusion may remain true.","A completed and independently accepted proof of the weakened statement, not merely an unsuccessful counterexample search.","A bounded counterexample result or necessity analysis that identifies the exact validity boundary.","At least one independently useful new application compared with retaining the original theorem and using a bespoke proof.","Precommitted proof-complexity, review-budget, maintenance, and rollback thresholds, followed by evidence that the generalization stays within them.","Willingness from the relevant author or repository maintainer to review and stage the result.","External prior-art research establishing whether the method or specific generalization is already known."],"next_evidence_step":"With an author or repository maintainer, select one theorem having at most four substantive hypotheses and precommit the object class, review budget, proof-complexity ceiling, usefulness test, and rollback trigger. Audit exactly one hypothesis, attempt a formally checkable weakened proof, and search the bounded class for counterexamples. Stage but do not deploy the result, then compare its valid coverage, proof effort, and interface complexity against the unchanged theorem plus a bespoke excluded-case proof and against one isolated alternative theorem. Falsify the intervention if a counterexample appears, the proof remains incomplete, no independent useful application is demonstrated, or any precommitted complexity or maintenance threshold is breached.","research_questions":["Which concrete theorem has an apparently nonminimal hypothesis and a tractable bounded class of excluded objects?","Does removing that single hypothesis admit a complete accepted proof, or does a counterexample or necessity argument establish its requirement?","Does the generalized statement support at least one independently useful application that otherwise requires a bespoke proof?","How do proof length, conceptual complexity, review time, and maintenance burden compare with the unchanged theorem and an isolated alternative?","Will the author or repository maintainer authorize staging while retaining the original theorem and enforcing rollback conditions?","What prior theorem-generalization, hypothesis-minimization, or formal-library refactoring work already addresses the same method or result?","Do downstream users interpret the broader theorem correctly, or does the more technical interface increase overapplication risk?"] ,"recommendation":"PARTNERED_RESEARCH","uncertainty_constraints":["The occurrence of overstrong hypotheses in any selected theorem family is a hypothesis, not an observed prevalence finding.","No concrete theorem, excluded object class, accepted weakened proof, or useful new application is supplied.","Downstream demand, avoided proof duplication, reuse, and maintenance savings are unmeasured.","Prior art, historical novelty, and prevalence of comparable methods are unverified.","Cost bands are resource-equivalent planning ranges based on a one-theorem pilot and not exact observed costs.","The economic deadweight-loss analogy does not establish mathematical value; sound applicability and avoided proof effort are only proxies.","Failed counterexample search cannot establish truth or replace a proof."],"closed_book_prior_art_boundary":"Prior art is unsearched and unverified in this closed-book assessment; no claim is made about novelty, prevalence, existing theorem-generalization methods, formal-library precedents, or whether the proposed weakening has already been proved."}