{"schema_version":1,"research_id":"eoa_inverse_innovation_exp06_external_evaluation_20260803","source_assessment_id":"bounded_rivalry_governance__mathematics:P1:v0","cell_id":"bounded_rivalry_governance__mathematics","search_queries":["formalizing mathematics proof assistant bottleneck mathematician time formalization project","site:darpa.mil expMath program formal mathematics 2025","Lean Blueprint formalization project dependency graph official","mathematics proof competition priority race strategic premature announcement research","Fermat Last Theorem Lean formalization project funding five years official","Lean Liquid Tensor Experiment formalization person years paper","Artificial Intelligence Mathematical Olympiad prize official rules Lean formal verification","site:leanprover-community.github.io mathlib contribution review pull requests formalization","site:gtr.ukri.org Fermat's Last Theorem Lean Buzzard grant","site:ukri.org Fermat Last Theorem Lean grant Kevin Buzzard","site:bls.gov mathematicians median wage 2025","site:leanprover-community.github.io lean blueprint documentation"],"sources":[{"source_id":"S1","title":"Contributing to mathlib","publisher":"Lean Prover Community","url":"https://leanprover-community.github.io/contribute/index.html","source_class":"OFFICIAL_GUIDANCE","publication_date":"2026","accessed_at":"2026-08-03","claims_supported":["Mathlib reported more than 2,600 open pull requests in mid-2026 and warned that review and merging may take time.","Maintainers sometimes must make hard scope decisions and encourage contributors to identify reviewers.","Mathlib requires maintainability and subject-expert supervision, showing that mechanically accepted Lean code does not eliminate expert-review costs."]},{"source_id":"S2","title":"Completion of the Liquid Tensor Experiment","publisher":"Lean Prover Community","url":"https://leanprover-community.github.io/blog/posts/lte-final/","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"2022-07-15","accessed_at":"2026-08-03","claims_supported":["A major research theorem was formally verified in Lean approximately eighteen months after the challenge was posed.","The project used a blueprint, numerous mathematical contributors, technical support, grants, servers, and a workshop.","Large collaborative formalization is feasible but consumes substantial specialist and coordination resources."]},{"source_id":"S3","title":"IMO Grand Challenge","publisher":"IMO Grand Challenge Committee","url":"https://imo-grand-challenge.github.io/","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"undated","accessed_at":"2026-08-03","claims_supported":["An existing mathematical challenge proposes machine-checkable Lean proof certificates, an explicit scoring target, a ten-minute certificate-checking limit, time limits, reproducibility requirements, and public rules.","Formal proof certificates and resource-bounded mathematical contests are established adjacent design elements.","The published rules remain a preliminary proposal rather than evidence that this candidate's route-selection process works."]},{"source_id":"S4","title":"Exponentiating Mathematics (expMath)","publisher":"Defense Advanced Research Projects Agency","url":"https://www.darpa.mil/research/programs/expmath-exponential-mathematics","source_class":"GOVERNMENT_OR_REGULATOR","publication_date":"2025","accessed_at":"2026-08-03","claims_supported":["DARPA funds and manages a program seeking professional-level mathematical evaluation, auto-decomposition, and autoformalization.","The program identifies a gap between current AI capabilities and pure-mathematics research and names a program manager and solicitation.","This establishes a credible funder with adjacent evaluation needs, but not expressed demand for a one-slot proof-route contest."]},{"source_id":"S5","title":"Formalising perfectoid spaces","publisher":"arXiv; authors Kevin Buzzard, Johan Commelin, and Patrick Massot","url":"https://arxiv.org/abs/1910.12320","source_class":"PRIMARY_RESEARCH","publication_date":"2019-10-27","accessed_at":"2026-08-03","claims_supported":["Lean handled definitions from sophisticated contemporary arithmetic geometry.","The authors estimated that formalizing the associated results with then-current technology would require many person-decades.","Mathematicians without computer-science training became proficient with a proof assistant, supporting technical feasibility while demonstrating scarce labor."]},{"source_id":"S6","title":"National employment and wage data by occupation, May 2025","publisher":"U.S. Bureau of Labor Statistics","url":"https://www.bls.gov/news.release/ocwage.t01.htm","source_class":"GOVERNMENT_OR_REGULATOR","publication_date":"2026-05","accessed_at":"2026-08-03","claims_supported":["The May 2025 mean wage for mathematicians was $62.15 per hour and $129,260 annually.","The mean annual wage for mathematical-science occupations was $119,880.","These wages provide a labor-cost anchor but exclude institutional overhead, scarce-specialist premiums, software, and opportunity cost."]},{"source_id":"S7","title":"Formalising Fermat","publisher":"UK Research and Innovation Gateway to Research","url":"https://gtr.ukri.org/projects?ref=EP%2FY022904%2F1","source_class":"GOVERNMENT_OR_REGULATOR","publication_date":"2024-09","accessed_at":"2026-08-03","claims_supported":["EPSRC awarded £934,043 for an active September 2024–September 2029 fellowship led by Kevin Buzzard at Imperial College London.","The project says too few mathematicians engage with proof assistants and describes full formalization as a gigantic task.","This supplies an actual funder, institution, principal investigator, project duration, and scale comparator, but not a budget for the proposed governance layer."]},{"source_id":"S8","title":"The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale","publisher":"Equational Theories Project Contributors","url":"https://teorth.github.io/equational_theories/paper.pdf","source_class":"PRIMARY_RESEARCH","publication_date":"2025-12","accessed_at":"2026-08-03","claims_supported":["A large collaborative project validated more than 22 million implication-graph edges in Lean while documenting organizational problems at scale.","The authors report difficulty allocating tasks, avoiding conflicting submissions, tracking progress, and verifying contributions from more than fifty participants.","Earlier projects assigned tasks first-come-first-served; the project automated task claims, reviews, continuous checks, replacement of proposed work, and dashboards.","Maintainers had limited time, administrative work was nontrivial, and inadequate early maintainer capacity caused hard-to-reverse design problems.","Blueprints, dependency graphs, version control, continuous integration, external checkers, contribution rules, and centralized communication are demonstrated implementation infrastructure."]}],"problem_evidence":{"support":"MODERATE","rationale":"The resource constraint and workflow problem are visible: mathlib reports a large review backlog; major formalizations take months to years; and the Equational Theories Project directly reports scarce maintainer time, conflicting submissions, task-allocation difficulty, and costly review. However, no source verifies the candidate's full causal story that a target consortium has exactly one route-level slot or that teams presently use premature completeness claims, concealed dependencies, excessive presentation, or withheld rival flaws to win it.","source_ids":["S1","S2","S5","S7","S8"]},"stakeholder_evidence":{"support":"MODERATE","rationale":"Credible adjacent authorizers and funders are identifiable: mathlib maintainers control merges, formalization-project organizers control task workflows, EPSRC funds a five-year formalization program, and DARPA manages a professional-mathematics evaluation program. They express needs for review capacity, formalized databases, maintainable workflows, and professional evaluation. None expresses demand for this specific bounded-rivalry mechanism, so adopter pull remains inferred rather than demonstrated.","source_ids":["S1","S4","S7","S8"]},"prior_art":{"proximity":"ADJACENT_PRIOR_ART","closest_analogues":[{"name":"Equational Theories Project contribution workflow","similarity":"Uses predefined goals, task claims, centralized records, Lean validation, pull-request review, continuous checks, contributor rules, and replaceable submissions to coordinate mathematical work under limited maintainer capacity.","remaining_difference":"It decomposes and collaboratively completes many tasks; it does not compare several complete proof routes for one scarce formalization slot using a correctness gate, secondary rubric, independent appeal, and reopening trigger.","source_ids":["S8"]},{"name":"Mathlib contribution and review process","similarity":"Places maintainability, integration, expert review, disclosure, and merge authority around formal Lean contributions while operating under a documented review backlog.","remaining_difference":"It reviews contributions for inclusion rather than awarding one scarce theorem-specific formalization slot among rival natural-language proof routes.","source_ids":["S1"]},{"name":"IMO Grand Challenge formal-to-formal rules","similarity":"Uses predeclared competition rules, machine-checkable Lean proof certificates, time and checking limits, reproducibility, and an explicit success threshold.","remaining_difference":"It evaluates AI performance on olympiad problems and requires already formal proofs; it does not triage informal research-proof routes for later specialist formalization or provide the proposed appeal and staged-reopening structure.","source_ids":["S3"]},{"name":"Liquid Tensor Experiment formalization challenge","similarity":"A named challenge mobilized a governed community, blueprint, specialist contributors, grants, servers, and a bounded theorem target culminating in formal verification.","remaining_difference":"It was a collaborative formalization effort rather than comparative selection among multiple proof routes for one slot.","source_ids":["S2"]}],"distinctive_claim_remaining":"For a consortium that truly has several plausible proof routes but capacity to formalize only one, a preregistered process combining a noncompensable reproduction gate, equal reviewer-facing resource limits, frozen secondary criteria, procedural appeal, and staged reopening will select a route with fewer downstream corrections or formalizer hours than blinded holistic triage or first-reproduced selection, without increasing total review burden beyond a preset budget or suppressing useful collaboration.","confidence":"HIGH"},"implementation_evidence":{"support":"STRONG","rationale":"Every core technical building block is demonstrated: Lean kernel checking, blueprints and dependency graphs, Git/version histories, contribution rules, dashboards, pull-request review, continuous integration, external checkers, and role-based project management. A de-identified shadow exercise is technically straightforward. Remaining uncertainties are rubric reliability, creation of realistic proof packets, protection of unpublished material, judge conflicts, and whether governance overhead defeats the scarce-capacity objective.","source_ids":["S1","S2","S3","S5","S8"]},"scores":{"meaningful_impact":{"score":3,"rationale":"Misallocation of scarce specialist formalization labor could waste months or years, but the affected setting is narrow and its prevalence is unmeasured.","source_ids":["S1","S2","S5","S7"]},"stakeholder_pull":{"score":2,"rationale":"Funders and maintainers visibly want scalable evaluation and formalization, but no organization requests this contest design.","source_ids":["S1","S4","S7","S8"]},"incremental_advantage":{"score":2,"rationale":"Correctness gating, equal access, appeal, and reopening plausibly improve first-come selection, but no comparative outcome evidence exists and collaboration may dominate rivalry.","source_ids":["S3","S8"]},"distinctiveness_plausibility":{"score":3,"rationale":"No exact match was found, although nearly every component exists in adjacent formalization workflows and mathematical challenges.","source_ids":["S1","S2","S3","S8"]},"technical_implementability":{"score":4,"rationale":"The required proof, provenance, dependency, workflow, and audit infrastructure already exists; the difficult work is expert judgment and governance calibration.","source_ids":["S1","S2","S3","S5","S8"]},"adoption_authority_feasibility":{"score":4,"rationale":"A consortium can govern its own funding slot, submission channel, judges, and formalizers, provided participation is consensual and publication and authorship remain outside the award.","source_ids":["S1","S4","S7","S8"]},"evidence_readiness":{"score":2,"rationale":"A bounded shadow test is ready to design, but problem prevalence, stakeholder willingness, rubric agreement, strategic behavior, and comparative effect require proprietary records or live expert testing.","source_ids":["S1","S8"]},"safety_net_benefit":{"score":4,"rationale":"De-identification, no stakes, a separate procedural review, preserved submissions, and an automatic return to an uncommitted state make the first test reversible.","source_ids":["S8"]},"scalability":{"score":2,"rationale":"Tooling scales contribution tracking, but correctness reproduction and route-quality judgment remain scarce expert activities; the cited project explicitly reports nontrivial administrative demands and limited maintainer time.","source_ids":["S1","S8"]}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Design and run one no-stakes shadow comparison with eight prepared packets, two small expert panels, independent lemma-chain audit, preregistration, analysis, and a short data-handling review.","confidence":"MODERATE","assumptions":["Existing settled-theorem materials can be adapted rather than created from scratch.","Approximately 100–250 expert and coordination hours are required.","Loaded specialist cost exceeds the BLS wage because institutional overhead and scarcity are included.","No participant prizes or new proof-assistant infrastructure are required."],"source_ids":["S6","S8"]},"initial_deployment_startup":{"band_2026_usd":"50K_TO_250K","scope":"Create a live-ready rulebook, proof-certificate schema, secure repository, conflict and appeal procedures, judge training, planted-gaming tests, and staged formalization gates.","confidence":"LOW","assumptions":["One theorem and one consortium are in scope.","Existing Lean, GitHub, blueprint, and continuous-integration infrastructure is reused.","Legal review is limited to consent, confidentiality, attribution, retention, and consortium authority.","The range excludes the value of the verification slot itself."],"source_ids":["S1","S6","S8"]},"operational_launch":{"band_2026_usd":"50K_TO_250K","scope":"Operate one consent-based live challenge through selection and its first staged formalization gate, including project management, judges, auditor, appeal reserve, and secure recordkeeping.","confidence":"LOW","assumptions":["Three to six specialist judges and auditors participate part-time.","Only correctness-passing routes receive secondary scoring.","No major proof route must be fully formalized merely to establish the initial correctness gate.","The formalization slot's underlying research cost is accounted for separately."],"source_ids":["S2","S6","S7","S8"]},"annual_recurring":{"band_2026_usd":"250K_TO_1M","scope":"Maintain governance and infrastructure and operate one or more theorem-route selections annually with expert review, audit, appeals, post-contest evaluation, and partial formalizer capacity.","confidence":"LOW","assumptions":["At least one specialist-equivalent role plus multiple part-time mathematical reviewers is needed.","The £934,043 five-year Formalising Fermat award is a scale comparator for a substantial formalization program, not a direct quote for this governance system.","The upper range allows scarce-domain expertise, institutional overhead, secure handling, and failed or reopened rounds.","Costs vary sharply with theorem complexity and cannot be inferred from wages alone."],"source_ids":["S2","S6","S7","S8"]}},"verified_pipeline_gates":{"externally_supported_problem":{"status":"YES","reason":"Scarce review capacity, long formalization timelines, conflicting submissions, task-allocation burdens, and limited maintainer time are externally documented. The more specific allegations of strategic concealment and premature completeness remain unverified subclaims.","source_ids":["S1","S2","S5","S8"]},"externally_credible_adopter_or_authorizer":{"status":"YES","reason":"Mathlib maintainers and formalization-project organizers possess relevant workflow authority, while EPSRC and DARPA are credible adjacent funders. Specific willingness to adopt this design is not established.","source_ids":["S1","S4","S7","S8"]},"distinct_testable_incremental_claim":{"status":"YES","reason":"The remaining claim compares the complete governed procedure against blinded holistic triage and first-reproduced selection on incorrect selections, correction burden, formalizer hours, reviewer hours, agreement, gaming survival, and collaboration effects.","source_ids":["S1","S3","S8"]},"bounded_next_evidence_step":{"status":"YES","reason":"An eight-packet, no-stakes, de-identified shadow comparison has finite inputs, explicit comparators, measurable outcomes, and preregisterable failure conditions.","source_ids":["S3","S8"]},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"The shadow step can be limited to an already-settled theorem, consenting experts, de-identified synthetic or licensed packets, and no funding, authorship, publication, employment, or reputational consequences. Unpublished live submissions should remain out of scope until confidentiality and attribution terms are approved.","source_ids":["S1","S8"]},"credible_cost_scope_and_range":{"status":"YES","reason":"The ranges state what is included and excluded and are anchored to government wage data, documented coordination burdens, and an actual five-year formalization award; precision remains low because no vendor or consortium quote exists.","source_ids":["S2","S6","S7","S8"]}},"next_evidence_step":"With one consenting formalization organization, preregister a no-stakes shadow comparison using eight de-identified packets derived from an already-settled theorem: at least two sound routes of different modularity, two known-gap routes, one undeclared-dependency route, one redundantly polished route, and two neutral controls. Randomly assign two conflict-screened panels to (A) the frozen correctness-gate-plus-secondary-rubric procedure and (B) blinded holistic triage; retain first-independently-reproduced as a logged third comparator. Separate auditors, blind to assignment, reproduce selected critical lemma chains. Measure false passage, selected-route correction count, estimated and subsequently observed formalizer hours on a fixed sample, reviewer minutes, inter-rater agreement, successful planted gaming, appeals, and evidence that participants would withhold collaboration. Falsify progression if any incorrect packet passes the gate, planted gaming determines selection, rubric agreement is below a preregistered threshold, the challenge fails to reduce correction or formalizer burden relative to both comparators, or governance hours exceed the preset shadow budget.","blocking_evidence":["No direct evidence establishes that a named consortium currently has several complete proof routes competing for exactly one formalization slot.","No prevalence data quantify premature completeness claims, concealed dependencies, excessive presentation, withheld rival flaws, or resulting misallocations.","No comparative field evidence shows that the proposed rubric outperforms blinded expert triage, first reproduction, lottery after correctness screening, or collaborative synthesis.","Expert inter-rater reliability, audit sensitivity, strategic adaptation, collaboration effects, and total governance overhead require live testing or proprietary workflow data.","No adopter has committed authority, staff, proof packets, or budget to a shadow exercise.","Confidentiality, attribution, retention, and access terms for unpublished proof routes remain unspecified.","Cost ranges are resource-equivalent estimates rather than consortium budgets or quotes."],"research_disposition":"PARTNERED_RESEARCH_PROGRAM","world_novelty_boundary":"World novelty, patentability, freedom to operate, market size, and realized impact are unmeasured. The search establishes only that no exact match appeared in the eight-source bounded review; it is not an exhaustive literature, product, legal, or patent search.","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_version":0,"controller_recommendation":{"action":"STOP_EMPIRICAL_RESEARCH_NEEDED","repairable":false,"material_progress_observed":true,"progress_targets":["Secure a consenting formalization organization and confirm from internal records that route-level scarcity and competing submissions actually occur.","Pre-register and execute the eight-packet shadow comparison against blinded holistic triage and first-independent-reproduction comparators.","Demonstrate zero incorrect passages, acceptable judge agreement, detection of planted gaming, and governance effort below the preset review budget.","Measure whether selected routes require fewer corrections or formalizer hours without reducing reported willingness to collaborate.","Approve confidentiality, attribution, retention, conflict, appeal, and publication terms before using any unpublished live proof route.","Replace resource-equivalent cost bands with a partner-specific staffing plan and budget after the shadow exercise."],"reason":"Bounded web research verified scarce expert-review capacity, credible adjacent authorizers, mature implementation components, and close prior practices, but it cannot establish the candidate's strategic-behavior prevalence or comparative effect. The decisive remaining evidence requires expert fieldwork, proprietary workflow records, and a live shadow test; under the controller rule this requires an empirical-research stop."},"proposal_index":1}