{"schema_version":1,"research_id":"eoa_inverse_innovation_exp06_external_evaluation_20260803","source_assessment_id":"catalytic_pathway_enablement__mathematics:P2:v0","cell_id":"catalytic_pathway_enablement__mathematics","search_queries":["cross-disciplinary mathematics collaboration terminology barriers proof research official report","site:aimath.org SQuaREs collaborative research teams mathematics","site:icerm.brown.edu collaboration mathematics research teams official","mathematics interdisciplinary collaboration communication barriers terminology study","ICERM Collaborate@ICERM official small groups mathematics research collaboration","NSF mathematics interdisciplinary collaboration solicitation terminology collaboration DMS","American Institute Mathematics focused collaborative research workshop official collaboration interdisciplinary","mathematics proof collaboration handoff terminology cross field","collaborative mathematics research communication terminology proof practices empirical study mathematicians","mathematicians collaboration practices proof writing division labor study","mathematical proof collaboration boundary objects terminology researchers","formal mathematics blueprint collaborative proof dependency graph Lean official","site:leanprover-community.github.io blueprint collaborative formalization dependency graph mathematics","Patrick Massot Lean blueprint collaborative mathematics project documentation","site:mathoverflow.net/help research level mathematics questions help center","site:bls.gov mathematicians median pay 2025","site:bls.gov/ooh/math/mathematicians-and-statisticians.htm median annual wage May 2025 mathematicians","BLS Occupational Employment Wage Statistics mathematicians 2025 hourly mean wage","site:bls.gov mathematicians May 2024 wage 15-2021"],"sources":[{"source_id":"S1","title":"Investigating communication hindrance in interdisciplinary collaboration: A grounded theory approach","publisher":"University of Arizona research portal; article published by the Association for Information Science and Technology/Wiley","url":"https://experts.arizona.edu/en/publications/investigating-communication-hindrance-in-interdisciplinary-collab/","source_class":"PRIMARY_RESEARCH","publication_date":"2016","accessed_at":"2026-08-03","claims_supported":["Interviews with eight interdisciplinary researchers identified domain disparity and divergent interpretations of shared artifacts as communication obstacles.","The study identified active and continuing learning as a mitigation strategy.","The sample was small and not specific to cross-subfield mathematical proof work."]},{"source_id":"S2","title":"Cultural barriers to interdisciplinary research collaboration: evidence from Australia","publisher":"Humanities and Social Sciences Communications, Springer Nature","url":"https://www.nature.com/articles/s41599-025-05196-x","source_class":"PRIMARY_RESEARCH","publication_date":"2025-06-11","accessed_at":"2026-08-03","claims_supported":["A survey of 430 academics and interviews with 14 university leaders found interdisciplinary collaboration common and documented language, communication, cultural, and search/networking barriers.","Eighty-five percent of survey participants said more cross-faculty networking opportunities would make them more inclined to collaborate outside their discipline.","Respondents explicitly described difficulty identifying appropriate collaborators, while leaders supported expanded interdisciplinary collaboration.","The evidence concerns broad interdisciplinarity, primarily an arts-science divide, rather than cross-subfield proof-obligation handoffs within mathematics."]},{"source_id":"S3","title":"SQuaREs: Structured Quartet Research Ensembles","publisher":"American Institute of Mathematics","url":"https://dev.aimath.org/squares/","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["AIM operates and financially supports repeated, focused collaborations of four to six mathematicians for up to three meetings over three years.","AIM is a credible mathematics-sector host or funder for small collaborative experiments.","SQuaREs fund substantive research teams, not a rotating proof-interface clinic or independent handoff service."]},{"source_id":"S4","title":"Collaborate@ICERM","publisher":"Institute for Computational and Experimental Research in Mathematics, Brown University","url":"https://icerm.brown.edu/collaborate","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["ICERM offers three-to-six-person research teams five-day residencies and provides computational infrastructure.","The program demonstrates institutional capacity to convene bounded mathematical collaborations and lists resulting publications.","Its required computational or experimental component and project-team model differ from the proposed human translation clinic."]},{"source_id":"S5","title":"How do I ask a good question?","publisher":"MathOverflow","url":"https://mathoverflow.net/help/how-to-ask","source_class":"OFFICIAL_GUIDANCE","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["MathOverflow already uses a reusable, governed intake pathway for research-level mathematics questions.","Its guidance requires prior search, supplied context, specificity, topical eligibility, and openness to inconclusive answers or cited support.","It is a public question-and-answer community rather than a confidential, dual-specialist service producing versioned lemma packets."]},{"source_id":"S6","title":"LeanArchitect: Automating Blueprint Generation for Humans and AI","publisher":"arXiv","url":"https://arxiv.org/abs/2601.22554","source_class":"PRIMARY_RESEARCH","publication_date":"2026-01-30","accessed_at":"2026-08-03","claims_supported":["Large Lean formalization projects already use structured dependency graphs linking informal mathematical exposition to formal declarations as collaboration and coordination tools.","LeanArchitect synchronizes declaration metadata, dependencies, proof status, and LaTeX representations and reports exposing inconsistencies in existing blueprints.","This is close prior art for statement fidelity and lemma dependency packets, but it presupposes formalization in Lean rather than cross-subfield human interpretation."]},{"source_id":"S7","title":"The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale","publisher":"arXiv","url":"https://arxiv.org/abs/2512.07087","source_class":"PRIMARY_RESEARCH","publication_date":"2025-12-08","accessed_at":"2026-08-03","claims_supported":["A large online mathematical collaboration combined human and automated proofs with Lean validation to determine an implication graph containing 22,028,942 edges among 4,694 equational laws.","The project demonstrates that explicit dependency structure, bounded proof tasks, shared tooling, and machine validation can coordinate mathematical work at scale.","Its formal, unusually enumerable domain and automated validation make it materially different from informal cross-subfield lemma translation."]},{"source_id":"S8","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":"2026-05-15","accessed_at":"2026-08-03","claims_supported":["BLS reports a May 2025 mean wage of $62.15 per hour and median wage of $60.92 per hour for the occupational category Mathematicians.","BLS reports a $91,550 annual mean wage for postsecondary mathematical-science teachers, although it does not publish an hourly value for that category.","These figures provide only a resource-equivalent labor anchor; specialist academic opportunity cost, benefits, overhead, and scarcity premiums remain uncertain."]}],"problem_evidence":{"support":"WEAK","rationale":"Two primary studies visibly support the broader phenomenon of disciplinary language, shared-artifact interpretation, networking, and collaborator-search barriers. However, neither measures proof-dependency registers, repeated hypothesis loss, lemma-handoff failures, or prevalence within cross-subfield mathematics projects. Existing mathematics programs establish that collaboration matters, not that this specific recurring obstruction is common or rate-limiting. The stated mathematics-specific problem therefore remains plausible but unverified.","source_ids":["S1","S2","S3","S4"]},"stakeholder_evidence":{"support":"MODERATE","rationale":"AIM and ICERM are identifiable mathematics organizations that fund and host bounded small-team collaboration, and MathOverflow operates a governed research-question intake community. The university study also records demand for central networking mechanisms. These are credible adopter or funder classes, but no source expresses demand for, commits to, or authorizes a rotating proof-interface clinic specifically.","source_ids":["S2","S3","S4","S5"]},"prior_art":{"proximity":"ADJACENT_PRIOR_ART","closest_analogues":[{"name":"MathOverflow research-question intake and expert community","similarity":"Uses eligibility, specificity, supplied context, community routing, citations, moderation, and reusable expert access for research-level mathematical questions.","remaining_difference":"It seeks public answers rather than producing confidential, versioned, independently fidelity-reviewed lemma handoff packets; it has no rotating paired-specialist workload or recovery cycle.","source_ids":["S5"]},{"name":"Lean blueprint and LeanArchitect workflows","similarity":"Represent definitions, lemmas, dependencies, proof status, and informal/formal correspondence in structured artifacts intended for distributed collaboration and consistency checking.","remaining_difference":"They require or support formalization in Lean and machine-checkable declarations; the proposal targets informal cross-subfield interpretation before proof work and expressly does not prove or certify the lemma.","source_ids":["S6"]},{"name":"Equational Theories Project","similarity":"Demonstrates decomposition of a mathematical program into explicit implication obligations coordinated across many contributors with formal validation.","remaining_difference":"The domain was highly enumerable and machine-checked, while the proposed clinic handles heterogeneous definitions, trust, attribution, confidential context, and recipient selection without formal verification.","source_ids":["S7"]},{"name":"AIM SQuaREs and Collaborate@ICERM","similarity":"Provide institutionally supported, bounded teams of mathematicians, concentrated sessions, facilities, and repeated or project-specific collaboration.","remaining_difference":"They convene teams to do substantive research; they do not operate a reusable cross-project translation lane with standardized intake, packet release, independent fidelity review, rotation, and queue governance.","source_ids":["S3","S4"]}],"distinctive_claim_remaining":"For archived, eligible obligations crossing the same two mathematical subfields, a capped rotating two-specialist clinic using a versioned lemma-packet contract will reduce total preparation labor or elapsed preparation time relative to an equal-access ad hoc handoff while producing no more material statement-fidelity defects, reopens, or inappropriate routings, and while correctly rejecting incompatible or substantively mathematical cases. This claim is contrastive and falsifiable but has not been tested.","confidence":"MODERATE"},"implementation_evidence":{"support":"MODERATE","rationale":"The constituent workflow is technically simple: secure intake records, templates, queues, versioning, blinded review, workload accounting, and rotation. Existing mathematical programs show that small specialist teams can be convened; MathOverflow shows structured intake; and Lean workflows show that explicit lemma/dependency artifacts can support coordination and expose inconsistencies. Feasibility gaps remain: no source verifies that a project has eight suitable archived obligations, permission to reuse confidential correspondence, willing paired specialists, stable cross-subfield mappings, or downstream reviewer capacity. Local owners can likely authorize shadow replay, but research-ethics, confidentiality, attribution, and record-use determinations must be made by the partner institution; no general legal clearance was established.","source_ids":["S2","S3","S4","S5","S6","S7","S8"]},"scores":{"meaningful_impact":{"score":3,"rationale":"If repeated interface failures are rate-limiting, avoiding lost hypotheses and duplicated specialist search could protect substantial research time and proof integrity. Mathematics-specific prevalence and aggregate consequence are unmeasured.","source_ids":["S1","S2"]},"stakeholder_pull":{"score":3,"rationale":"Credible mathematics institutions fund focused collaboration, and broader interdisciplinary researchers express demand for networking and routing support, but there is no clinic-specific request or committed partner.","source_ids":["S2","S3","S4"]},"incremental_advantage":{"score":2,"rationale":"The proposal combines useful controls, but no evidence shows it outperforms direct consultation, MathOverflow-style intake, a shared glossary, an ordinary focused team, or blueprint/formalization workflows under equal labor.","source_ids":["S3","S4","S5","S6","S7"]},"distinctiveness_plausibility":{"score":3,"rationale":"No exact rotating human lemma-interface clinic was found, while several components have close analogues. Distinctiveness is plausible only at the level of the governed combination and comparator-defined claim, not the individual mechanisms.","source_ids":["S3","S4","S5","S6","S7"]},"technical_implementability":{"score":4,"rationale":"A shadow replay requires ordinary document, queue, access-control, and review tooling rather than new mathematical infrastructure. The hard dependency is scarce specialist judgment and suitable records, not technology.","source_ids":["S3","S4","S5","S6","S8"]},"adoption_authority_feasibility":{"score":3,"rationale":"A project steering group can plausibly authorize a local shadow replay, and AIM or ICERM are credible conveners. No external source confirms authority over a suitable archive or willingness to sponsor this exact experiment.","source_ids":["S3","S4"]},"evidence_readiness":{"score":2,"rationale":"The proposed eight-case replay is bounded and measurable, but the existence, comparability, permissions, and representativeness of the required archived cases are not externally established.","source_ids":["S6","S7"]},"safety_net_benefit":{"score":4,"rationale":"Shadow use of resolved cases, concealed resolutions, independent fidelity review, no live theorem authority, and rollback to original records substantially limit mathematical and organizational harm. Confidentiality and attribution risks still require local controls.","source_ids":["S2"]},"scalability":{"score":2,"rationale":"Templates and routing can be reused, but dual-subfield specialists, independent reviewers, conflict management, and recovery time scale with cases; rotation may reduce continuity, and existing small-team programs do not establish high-throughput operation.","source_ids":["S3","S4","S6"]}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Pre-register and execute one eight-case archived shadow replay with a rotating two-specialist clinic, equal-access ad hoc comparator, blinded fidelity reviewers, secure records, analysis, and a short report.","confidence":"MODERATE","assumptions":["Approximately 200-400 total specialist, comparator, reviewer, coordinator, and analysis hours.","BLS mathematician wages near $61-$62 per hour are used only as a direct-labor anchor; benefits, institutional overhead, and scarcity premiums are added within the band.","Suitable archived cases already exist and do not require costly digitization or legal discovery.","No travel or custom software development is required."],"source_ids":["S8"]},"initial_deployment_startup":{"band_2026_usd":"10K_TO_50K","scope":"Design and approve the intake contract, lemma-packet template, glossary/version controls, conflict and confidentiality rules, secure repository, basic queue dashboard, training, and withdrawal procedures for one project.","confidence":"LOW","assumptions":["Uses existing document, issue-tracking, and identity-management systems.","Requires roughly 200-500 hours across mathematical leads, coordinator, information security, and administration.","Does not include live clinic casework or formal proof-assistant migration."],"source_ids":["S5","S6","S8"]},"operational_launch":{"band_2026_usd":"50K_TO_250K","scope":"Run a voluntary, monitored clinic for one substantial collaboration for 6-12 months, including coordinator capacity, rotating specialist stipends or buyout, independent review, secure administration, and evaluation.","confidence":"LOW","assumptions":["Roughly 0.5-1.5 full-time resource-equivalents distributed across coordination, specialists, review, and governance.","Specialists are compensated rather than relying on hidden unpaid labor.","No dedicated facility, travel program, or full formalization platform is purchased."],"source_ids":["S3","S4","S8"]},"annual_recurring":{"band_2026_usd":"50K_TO_250K","scope":"Maintain a one-project clinic with rotation, compensated sessions, independent review sampling, glossary and template refresh, access controls, incident response, and annual evaluation.","confidence":"LOW","assumptions":["Approximately 800-2,400 compensated hours per year across all roles.","Case volume remains bounded to specialist and downstream-review capacity.","Existing institutional software and records infrastructure remain available.","The range excludes multi-institution scale, travel residencies, and substantive proof labor."],"source_ids":["S3","S4","S8"]}},"verified_pipeline_gates":{"externally_supported_problem":{"status":"UNCERTAIN","reason":"External evidence supports broad interdisciplinary communication and routing barriers, but not the prevalence or importance of repeated cross-subfield lemma-handoff stalls in collaborative mathematics.","source_ids":["S1","S2"]},"externally_credible_adopter_or_authorizer":{"status":"UNCERTAIN","reason":"AIM and ICERM are credible mathematics conveners and funders, and a project steering group is a plausible local authorizer, but no source identifies a willing host with authority over suitable proof records or expresses demand for this clinic.","source_ids":["S3","S4"]},"distinct_testable_incremental_claim":{"status":"YES","reason":"The claim compares a capped rotating clinic with an equal-access ad hoc handoff on fidelity, labor, time, reopens, routing, and specialist rotation under fixed mathematical standards.","source_ids":["S5","S6","S7"]},"bounded_next_evidence_step":{"status":"YES","reason":"An eight-case concealed archival replay with a contemporaneous comparator, one incompatible case, blinded fidelity review, session caps, and precommitted stop criteria is bounded in cases, authority, duration, and harm.","source_ids":["S6","S7"]},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"A shadow replay on resolved cases need not alter theorem status, and local owners can retain all mathematical authority. Proceeding still requires record-owner permission, confidentiality controls, conflict checks, and any locally required ethics determination before data access.","source_ids":["S2"]},"credible_cost_scope_and_range":{"status":"YES","reason":"All four scopes are bounded and their labor assumptions are explicit; current BLS wages provide a public resource-equivalent anchor. Confidence remains low outside the first test because specialist scarcity and institutional overhead are unknown.","source_ids":["S8"]}},"next_evidence_step":"Secure one willing collaborative mathematics project and eight authorized, de-identified, fully resolved obligations spanning the same subfield pair, including successful translations, substantive-mathematics cases, and one deliberately incompatible case. Before access, pre-register eligibility, random ordering, equal source access, a fixed session cap, specialist rotation after two cases, confidentiality and attribution rules, and immediate-stop conditions. Compare a rotating two-specialist clinic with a separate ad hoc-handoff team using matched total access and recorded labor. Conceal archived resolutions until both packets are frozen. Independent reviewers blinded to arm should score exact statement fidelity, preserved definitions, hypotheses and quantifiers, explicit uncertainty, suitable routing, readiness for ordinary proof review, material defects, reopens, total labor, elapsed preparation, and downstream review burden. Falsify the intervention for this scope if either arm reveals a confidentiality breach; the clinic introduces any material undisclosed statement alteration; it fails to reject the incompatible case; more than half of nominally eligible cases require substantive escalation; median total preparation labor and elapsed time show neither a precommitted 25% improvement nor another precommitted practically meaningful gain over ad hoc handoff; or reopens, defects, or downstream burden increase. Passing this exploratory test would justify a larger multi-project trial, not live mandatory intake.","blocking_evidence":["No mathematics-specific audit establishes how often cross-subfield obligations stall because of repeated translation and routing rather than missing mathematical insight.","No project, AIM program, ICERM program, or other institution has committed to adopt, authorize, or fund the clinic.","The existence, comparability, ownership, confidentiality status, and reuse permission of an eight-case archived corpus are unverified.","No comparative evidence shows that the clinic preserves fidelity or reduces total labor, elapsed preparation, reopens, or downstream burden relative to ad hoc handoffs.","Specialist willingness, fair compensation, rotation continuity, conflict handling, and downstream reviewer capacity require field verification.","Local determination of research-ethics review, confidentiality handling, attribution protection, and permissible use of archived correspondence is unresolved."],"research_disposition":"PARTNERED_RESEARCH_PROGRAM","world_novelty_boundary":"The search found adjacent institutional collaboration programs, structured research-question intake, formal proof blueprints, and large machine-assisted mathematical collaboration, but no exact rotating proof-interface clinic. This does not establish world novelty, patentability, freedom to operate, market size, or realized impact; those remain unmeasured.","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_version":0,"controller_recommendation":{"action":"STOP_EMPIRICAL_RESEARCH_NEEDED","repairable":false,"material_progress_observed":true,"progress_targets":["Obtain written authorization from a mathematics-project owner and confirm eight suitable de-identified archived obligations with lawful and ethical permission for controlled reuse.","Pre-register the clinic-versus-ad-hoc replay, matched access and labor rules, blinded fidelity rubric, practical-effect threshold, confidentiality controls, and falsifiers.","Execute the eight-case replay and report case-level fidelity defects, hypothesis or quantifier changes, routing accuracy, escalation, labor, elapsed time, reopens, downstream burden, and specialist-rotation effects.","Document specialist compensation, workload, conflicts, recovery, continuity, and whether the incompatible case is correctly rejected.","Obtain a written post-test adoption decision from an authorized project steering group or credible mathematics institute before any live or mandatory deployment."],"reason":"Bounded web research establishes plausibility, identifies credible adjacent practices and institutions, and sharply defines the incremental claim. It cannot answer the decisive questions: mathematics-specific prevalence, archive availability, comparative fidelity and efficiency, human workload, or adopter commitment. Those require proprietary records, partner authorization, and a controlled human replay. Under the required controller rule, this empirical-research stop is non-repairable within the web-research pipeline."},"proposal_index":2}