{"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 to determine whether a single hypothesis can be removed while preserving its conclusion, then stage a proved generalization beside the original theorem. The proposed value is broader sound applicability and less bespoke proof work, but the packet supplies neither a concrete theorem instance nor evidence of downstream usefulness or novelty.","adopter_authorizer":"A theorem author or formal-repository maintainer can authorize staging and review; acceptance still requires a valid proof under the relevant mathematical or formal system.","scores":{"meaningful_impact":{"score":3,"rationale":"A valid generalization could expand reusable theorem coverage and avoid duplicated proofs, but the packet provides no concrete theorem, excluded application, prevalence evidence, or measured burden."},"stakeholder_pull":{"score":2,"rationale":"Theorem authors, downstream mathematicians, and library maintainers are identified, but repeated bespoke work and demand for a generalized result are explicitly hypotheses rather than observed pull."},"incremental_advantage":{"score":4,"rationale":"Relative to unchanged theorems or isolated variants, auditing one assumption and publishing a proved generalization offers a clear route to reusable coverage while retaining the original theorem; the advantage remains conditional on finding a useful weakening."},"distinctiveness_plausibility":{"score":2,"rationale":"Systematic assumption minimization is coherently specified, but prior art is unsearched and the packet cannot establish that this practice or library pattern is distinctive."},"technical_implementability":{"score":4,"rationale":"The pilot is technically bounded to one theorem, one hypothesis, a proof attempt, and counterexample checks, using ordinary mathematical and formal-library activities; hidden dependencies or difficult proof reconstruction could still defeat it."},"adoption_authority_feasibility":{"score":4,"rationale":"The theorem author or repository maintainer is a plausible authorizer, and staging beside the original limits the decision required; final acceptance remains contingent on proof and review."},"evidence_readiness":{"score":3,"rationale":"The candidate supplies separate problem and intervention falsifiers plus halt conditions, but it lacks a named theorem family, admissible object class, review budget, and precommitted usefulness and complexity thresholds."},"safety_net_benefit":{"score":4,"rationale":"The original theorem remains available, proof validity is non-negotiable, failed counterexample search is not treated as proof, and staged changes can be withdrawn; incomplete review could still permit misuse or maintenance burden."},"scalability":{"score":3,"rationale":"The audit pattern could be repeated across theorem families, but each generalization requires theorem-specific proof work, counterexample analysis, review, and maintenance, so scalable benefit is uncertain."}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Select one theorem with no more than four substantive hypotheses, audit one hypothesis, attempt a weakened proof, examine a bounded object class for counterexamples, and assess one candidate new application without changing the published interface.","confidence":"LOW","assumptions":["One qualified mathematician or formalizer performs several weeks of work.","The theorem and relevant object class are accessible without paid proprietary data.","The proof does not require major new infrastructure or extensive mechanization.","Independent review and prior-art checking are limited in scope."]},"initial_deployment_startup":{"band_2026_usd":"10K_TO_50K","scope":"Formalize or package one successful weakened theorem, document its relationship to the original, add checks and examples, obtain repository review, and stage it beside the unchanged theorem.","confidence":"LOW","assumptions":["Only one theorem and one repository are involved.","Existing proof-assistant, version-control, and continuous-integration infrastructure is usable.","No foundational library redesign is required.","Author and maintainer coordination remains limited."]},"operational_launch":{"band_2026_usd":"10K_TO_50K","scope":"Accept and publish the reviewed generalization in one library or theorem collection, validate at least one independent application, document usage boundaries, and monitor initial misuse and maintenance signals.","confidence":"LOW","assumptions":["The proof and application survive review.","Launch remains confined to one repository or theorem family.","No migration of existing users is mandatory because the original theorem is retained.","Complexity stays below a precommitted threshold."]},"annual_recurring":{"band_2026_usd":"UNDER_10K","scope":"Maintain the added theorem interface, respond to issues, update proof dependencies, and periodically review reuse, misuse, and maintenance burden for the single accepted generalization.","confidence":"LOW","assumptions":["Only one generalized theorem is maintained.","Dependency churn is modest.","No recurring dedicated research program or broad user-support function is included.","The interface does not generate substantial downstream breakage."]}},"research_burden":"HIGH","earliest_credible_horizon":"3_TO_12_MONTHS","pipeline_gates":{"recognizable_externally_supportable_problem":{"status":"YES","reason":"An unnecessarily strong hypothesis excluding objects for which the conclusion is true is a recognizable mathematical problem with observable manifestations such as bespoke variants and blocked theorem reuse, although its occurrence in any selected family remains unverified."},"identifiable_adopter_or_authorizer":{"status":"YES","reason":"The candidate explicitly identifies theorem authors and repository maintainers as pilot authorizers, with mathematical acceptance controlled by proof and review."},"distinct_testable_incremental_claim":{"status":"YES","reason":"The candidate claims that removing one unnecessary hypothesis can produce a proved theorem covering at least one independently useful excluded application, compared with retaining the original theorem or proving an isolated special-case result."},"bounded_next_evidence_step":{"status":"YES","reason":"The authorized step is limited to one theorem with at most four hypotheses, one audited assumption, one weakened proof attempt, a bounded counterexample search, and staging without replacing the original."},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"Proof validity is protected, the original theorem is retained, failed search is not accepted as proof, and explicit halt and rollback conditions cover counterexamples, failed proofs, hidden dependencies, and excess review cost."},"implementation_cost_scope_and_range":{"status":"UNCERTAIN","reason":"The activity categories are identifiable, but no theorem, proof system, object class, complexity threshold, review budget, or repository has been selected, so implementation resources cannot be supported beyond a low-confidence broad band."}},"blocking_evidence":["A concrete theorem whose hypotheses may be nonminimal over a specified domain.","A completed proof of the single-hypothesis weakening or a necessity result showing that weakening is impossible.","Counterexample results for a predeclared bounded object class, without treating absence of discovered counterexamples as proof.","At least one independently useful application admitted by the weakened theorem but not directly by the original statement.","Precommitted proof-complexity, review-cost, and maintenance thresholds.","Evidence of stakeholder demand or repeated bespoke proof work in the selected theorem family.","Prior-art findings on hypothesis minimization, theorem generalization, and formal-library refactoring."],"next_evidence_step":"Choose one concrete theorem with at most four substantive hypotheses and predeclare one target hypothesis, a bounded object class, one candidate excluded application, and complexity and review limits. Attempt a proof of the singly weakened statement and compare it with the unchanged-theorem/bespoke-proof baseline; falsify the opportunity if a counterexample or necessity proof appears, the proof fails, no independently useful new application results, or any preset complexity or review threshold is exceeded. Stage any result privately beside the original theorem pending independent review.","research_questions":["Is one stated hypothesis unnecessary for the conclusion over the predeclared domain?","Does the weakened statement admit at least one independently useful application excluded by the original theorem?","Does the generalized theorem reduce total proof effort relative to a bespoke proof for that application?","Does proof, interface, review, or maintenance complexity exceed the preset threshold?","Do theorem authors, downstream users, or maintainers report a concrete need for the added applicability?","What prior methods or generalized statements already address the same hypothesis boundary?","Can users apply the generalized interface correctly without increasing misuse or support burden?"],"recommendation":"VALIDATE_PROBLEM_FIRST","uncertainty_constraints":["The occurrence of overstrong hypotheses in the selected theorem family is only a hypothesis.","No theorem family, theorem instance, excluded object, or independent application is named.","Downstream demand, duplicated effort, and realized reuse are unmeasured.","Prior art is explicitly unsearched, so novelty and distinctiveness cannot be inferred.","Cost bands are resource-equivalent planning ranges, not observed or quoted costs.","Proof difficulty, formalization requirements, review burden, and maintenance load depend strongly on the theorem selected.","Counterexample search alone cannot establish validity or hypothesis dispensability."],"closed_book_prior_art_boundary":"No external search was performed. The assessment makes no claim about historical novelty, prevalence, existing hypothesis-minimization methods, analogous theorem generalizations, formal-library precedents, market size, realized impact, or exact cost."}