{"schema_version":1,"research_id":"eoa_inverse_innovation_exp06_external_evaluation_20260803","source_assessment_id":"ritualized_meaning_and_commitment_enactment__mathematics:P1:v0","cell_id":"ritualized_meaning_and_commitment_enactment__mathematics","search_queries":["site:ams.org collaborative mathematics proof errors long proof verification responsibility","site:leanprover-community.github.io mathlib contribution review maintainers documentation","site:stacks.math.columbia.edu project proof tags maintenance contributors","mathematical proof peer review errors long collaborative proofs formal verification","Mathematical proof between generations arxiv Bayer Benzmuller Buzzard proof collaboration generations","Polymath project collaborative mathematics proof project organization paper","site:nasa.gov after action review guide lessons learned debrief","site:hhs.gov OHRP quality improvement human subjects research IRB determination","Stacks Project contribution guidelines tags corrections proof collaborative official","site:docs.github.com issues assigning assignees milestones task lists project tracking official","site:bls.gov OEWS mathematicians hourly mean wage May 2025","research ritual organizational commitment workplace empirical study collective ritual","site:stacks.math.columbia.edu \"contribute\" \"The Stacks project\"","site:stacks.math.columbia.edu \"comments\" \"proof\" Stacks project","site:stacks.math.columbia.edu/about Stacks project collaborative textbook corrections","BLS mathematicians 15-2021 May 2025 wages","site:bls.gov/oes/2025/may/oes251022.htm mathematical science teachers postsecondary May 2025","site:bls.gov/oes/2025/may/oes152021.htm mathematicians","May 2025 OEWS 15-2021 mathematicians mean annual wage"],"sources":[{"source_id":"S1","title":"Checking correctness in mathematical peer review","publisher":"SAGE Publications, Social Studies of Science","url":"https://journals.sagepub.com/doi/10.1177/03063127231200274","source_class":"PRIMARY_RESEARCH","publication_date":"2023-09-30","accessed_at":"2026-08-03","claims_supported":["A study using 95 editor interviews and more than 100 referee reports found that published mathematics contains mistakes, proof checking is difficult, and peer review adds confidence without guaranteeing correctness.","Editors reported referee scarcity and stress in mathematical peer review.","Mathematical correctness is established through continuing scrutiny and community use, not merely publication or collective confidence."]},{"source_id":"S2","title":"Mathematical Proof Between Generations","publisher":"arXiv","url":"https://arxiv.org/abs/2207.04779","source_class":"PRIMARY_RESEARCH","publication_date":"2022-07-08","accessed_at":"2026-08-03","claims_supported":["Contemporary proofs can exceed comfortable human comprehensibility and differ materially between theoretical definitions and ordinary practice.","Proof assistants are a credible alternative or complement for precision and intergenerational transmission, but they address derivational verification rather than the proposed social renewal mechanism."]},{"source_id":"S3","title":"Pull Request Review Guide","publisher":"Lean Prover Community","url":"https://leanprover-community.github.io/contribute/pr-review.html","source_class":"OFFICIAL_PRODUCT_DOCUMENTATION","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["Mathlib already distributes review across contributors while reserving merge authority to maintainers.","Partial reviews are explicitly useful, review roles differ in authority, and humility and respectful challenge are documented workflow expectations.","This is close prior art for distributed proof stewardship without a ritualized renewal layer."]},{"source_id":"S4","title":"About—The Stacks project","publisher":"The Stacks Project","url":"https://stacks.math.columbia.edu/about","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["The Stacks Project is a long-lived collaborative mathematical reference with a named maintainer who accepts contributor changes.","Permanent tags, hyperlinks, and search expose dependencies among lemmas and theorems.","Its maintained dependency infrastructure is close prior art for durable proof memory and stewardship without periodic symbolic re-consent."]},{"source_id":"S5","title":"After Action Review (Pause and Learn)","publisher":"NASA APPEL Knowledge Services","url":"https://appel.nasa.gov/wp-content/uploads/2015/11/After-Action-Review.pdf","source_class":"OFFICIAL_GUIDANCE","publication_date":"2015-11","accessed_at":"2026-08-03","claims_supported":["After-action reviews are an established structured practice for capturing knowledge from activities and sharing lessons across teams.","A short post-session debrief and organizational-memory function therefore are established adjacent practice rather than novel components."]},{"source_id":"S6","title":"Work group rituals enhance the meaning of work","publisher":"Organizational Behavior and Human Decision Processes / Harvard Business School","url":"https://www.hbs.edu/ris/Publication%20Files/Work%20group%20rituals%20enhance%20the%20meaning%20of%20work_f16ec05d-eecb-48c2-b13a-bb09fe166dbe.pdf","source_class":"PRIMARY_RESEARCH","publication_date":"2021-07","accessed_at":"2026-08-03","claims_supported":["Five studies involving 1,099 participants associated group-ritual features with greater task meaningfulness and some subsequent prosocial work behavior.","Reported effects ranged from negligible to medium and varied by context, so general ritual benefits cannot be assumed for mathematical proof stewardship.","The study establishes group ritual as prior research but does not test proof-obligation ownership, consent-sensitive refusal, or theorem-certification confusion."]},{"source_id":"S7","title":"Quality Improvement Activities FAQs","publisher":"U.S. Department of Health and Human Services, Office for Human Research Protections","url":"https://www.hhs.gov/ohrp/regulations-and-policy/guidance/faq/quality-improvement-activities/index.html","source_class":"GOVERNMENT_OR_REGULATOR","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["A systematic intervention evaluation intended to contribute to generalizable knowledge may be human-subjects research even when framed as quality improvement.","IRB review may be required when covered research is non-exempt and involves human subjects; publication intent alone does not decide the classification.","A site-specific research/IRB determination is therefore an unresolved prerequisite before treating anonymous participant feedback as research data."]},{"source_id":"S8","title":"Table 1. National employment and wage data from the Occupational Employment and Wage Statistics survey by occupation, May 2025","publisher":"U.S. Bureau of Labor Statistics","url":"https://www.bls.gov/news.release/ocwage.t01.htm","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"2026-05-15","accessed_at":"2026-08-03","claims_supported":["The May 2025 national mean wage was $62.15 per hour for mathematicians and $129,260 annually.","The annual mean for postsecondary mathematical-science teachers was $91,550.","These figures support order-of-magnitude opportunity-cost calculations, while benefits, overhead, geography, and seniority require explicit multipliers."]}],"problem_evidence":{"support":"MODERATE","rationale":"Direct qualitative evidence establishes that mathematical proofs can contain consequential mistakes, checking is difficult, peer review is stressed, and confidence develops through continued scrutiny. Official mathlib and Stacks practices confirm that large mathematical artifacts require distributed review, maintainers, persistent identifiers, and dependency navigation. None of the eight sources directly measures the candidate's narrower condition: qualified proof obligations becoming socially unowned specifically because collaborators depart. That prevalence and causal pathway remain unverified.","source_ids":["S1","S2","S3","S4"]},"stakeholder_evidence":{"support":"WEAK","rationale":"Mathlib maintainers and the Stacks Project maintainer are identifiable examples of actors with authority over collaborative mathematical artifacts, and both publicly invite distributed review or contribution. They express demand for reviewing and maintenance, not for a recurring ritual or for renewal of proof-obligation ownership. No collaboration, funder, editor, or maintainer was found requesting or agreeing to test this intervention.","source_ids":["S3","S4"]},"prior_art":{"proximity":"ADJACENT_PRIOR_ART","closest_analogues":[{"name":"Mathlib pull-request review and maintainer workflow","similarity":"Distributes review, permits partial contributions, documents role authority, and converts review into an auditable merge decision.","remaining_difference":"It does not periodically re-consent owners of inherited informal obligations, use symbolic marking, or separately audit whether refusal felt costly.","source_ids":["S3"]},{"name":"Stacks Project tagged dependency and maintainer model","similarity":"Maintains a long-lived collaborative mathematical artifact using durable result identifiers, navigable dependencies, contributor input, and a named decision authority.","remaining_difference":"It provides continuous technical infrastructure rather than a marked, recurring, consent-governed renewal of stewardship.","source_ids":["S4"]},{"name":"Mathematical peer review and proof-assistant formalization","similarity":"Both directly address confidence in proof correctness and transmission of sophisticated proofs across people and time.","remaining_difference":"Peer review and proof assistants evaluate arguments; the proposal expressly limits itself to ownership and memory of outstanding human checking obligations.","source_ids":["S1","S2"]},{"name":"NASA After Action Review plus established workplace group rituals","similarity":"AARs capture lessons after bounded activity, while group-ritual research supplies marked collective action intended to transfer meaning to work.","remaining_difference":"The sources do not combine these elements with proof-dependency ledgers, costless refusal, non-certification safeguards, or explicit retirement in a mathematics collaboration.","source_ids":["S5","S6"]}],"distinctive_claim_remaining":"For a collaboration with at least one documented qualified or ambiguously owned proof dependency, adding a voluntary, explicitly non-certifying marked enactment to an otherwise matched obligation-review workflow will produce more accurate accepted/revised/declined ownership records and better seven-day unaided recall of the obligation's status and owner, without increasing perceived pressure to speak or mistaken belief that the theorem was certified. Equality or superiority of the plain workflow, conspicuous refusal, inaccurate ledger conversion, or increased certification confusion falsifies the incremental claim.","confidence":"MODERATE"},"implementation_evidence":{"support":"MODERATE","rationale":"The intervention requires no new mathematical or software capability: existing review roles, persistent dependency identifiers, ledgers, facilitation, and short debriefs are established practices. A 25-minute session is operationally plausible and inexpensive relative to mathematician labor. Feasibility is not yet demonstrated in a live collaboration, however. The main workflow risks are prestige capture, compelled visibility, confusion between stewardship and correctness, disclosure of unpublished technical information, and ritual overhead. Authority must remain with the collaboration's technical governance, while an independent consent monitor can stop the session but cannot certify mathematics. A site-specific determination is needed on institutional policy, privacy, employment implications, and whether systematic feedback collection requires human-subjects review.","source_ids":["S3","S4","S5","S6","S7","S8"]},"scores":{"meaningful_impact":{"score":3,"rationale":"Preventing unowned dependencies and false confidence could protect downstream mathematical work, but the intervention does not verify proofs and the prevalence of turnover-caused ownership failure is unknown.","source_ids":["S1","S2"]},"stakeholder_pull":{"score":2,"rationale":"Credible maintenance authorities and review communities exist, but none expressed demand for the ritualized layer or agreed to adopt it.","source_ids":["S3","S4"]},"incremental_advantage":{"score":2,"rationale":"Ledgers, tagged dependencies, ordinary review, maintainers, and debriefs already provide most operational functions; only a matched field test can show that symbolic enactment adds value rather than pressure and overhead.","source_ids":["S3","S4","S5"]},"distinctiveness_plausibility":{"score":3,"rationale":"No exact proof-obligation renewal rite was found, and the non-certifying, refusal-preserving integration is contrastive; nevertheless, every principal component has close adjacent precedent.","source_ids":["S3","S4","S5","S6"]},"technical_implementability":{"score":5,"rationale":"The pilot uses ordinary documents, a dependency ledger, a turn marker, facilitation, and surveys; no new technical system is necessary.","source_ids":["S3","S4","S5"]},"adoption_authority_feasibility":{"score":3,"rationale":"A collaboration's existing maintainer or governance body can authorize a pilot, but no named site has consented and institutional research/privacy determinations may be required.","source_ids":["S3","S4","S7"]},"evidence_readiness":{"score":4,"rationale":"The claim has a matched comparator, observable ledger outputs, immediate safety measures, seven-day recall, and clear falsifiers; obtaining a willing field site is the principal missing input.","source_ids":["S5","S7"]},"safety_net_benefit":{"score":3,"rationale":"Explicit non-certification language, costless passing, witnessed unresolved items, and rollback could expose ambiguity before downstream reliance, but collective ceremony can itself manufacture confidence or professional pressure.","source_ids":["S1","S6","S7"]},"scalability":{"score":3,"rationale":"Materials and facilitation are lightweight, but legitimacy, hierarchy, cultural response to ritual, confidentiality, and governance must be re-established in each collaboration.","source_ids":["S3","S4","S6"]}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"UNDER_10K","scope":"Prepare and run one ritual session and one time-matched plain comparison at one collaboration, involving approximately 8-12 participants; administer anonymous immediate measures, score ledger accuracy, and conduct one seven-day recall check.","confidence":"MODERATE","assumptions":["Approximately 50-75 total participant, facilitator, preparation, and analysis hours.","Resource equivalence uses roughly $60-$125 per hour, anchored to the $62.15 May 2025 mean mathematician wage and allowing for 2026 escalation and institutional overhead.","Existing meeting, survey, and ledger tools are used; no software procurement or external travel.","Any formal IRB process beyond a brief institutional determination could move this into the 10K_TO_50K band."],"source_ids":["S7","S8"]},"initial_deployment_startup":{"band_2026_usd":"10K_TO_50K","scope":"Adapt the protocol, consent and accessibility checks, ledger fields, training, privacy rules, stop procedures, and evaluation instruments for one institution or long-lived collaboration.","confidence":"MODERATE","assumptions":["Approximately 150-300 hours across mathematical maintainers, a facilitator, project administration, and institutional ethics/privacy review.","No bespoke software integration, legal dispute, or paid external cultural consultation is required.","The collaboration already has a usable dependency ledger and governance body."],"source_ids":["S3","S4","S7","S8"]},"operational_launch":{"band_2026_usd":"10K_TO_50K","scope":"Run, monitor, and revise three to five milestone sessions in one collaboration, including independent consent monitoring, debrief analysis, artifact follow-up, and a keep/adapt/retire review.","confidence":"MODERATE","assumptions":["Approximately 200-400 total hours across participants and support roles.","Sessions attach to existing milestones and use existing infrastructure.","No mathematical verification work is charged to the intervention except the time required to identify and record its artifacts."],"source_ids":["S3","S5","S8"]},"annual_recurring":{"band_2026_usd":"10K_TO_50K","scope":"Maintain a quarterly or milestone-triggered cycle for one collaboration, with facilitator rotation, ledger administration, debriefs, an annual harm audit, and retirement readiness.","confidence":"LOW","assumptions":["Approximately 100-250 annual hours depending on collaboration size and cadence.","Loaded labor is valued above direct wage to include benefits and overhead.","The estimate excludes the underlying cost of checking proofs and producing promised verification artifacts.","Costs could remain UNDER_10K for a small volunteer collaboration or exceed this band for a large, highly paid, multi-institutional team."],"source_ids":["S5","S8"]}},"verified_pipeline_gates":{"externally_supported_problem":{"status":"YES","reason":"Research and first-party mathematical projects establish difficult proof checking, residual errors, distributed review, and long-lived dependency maintenance, although turnover-specific prevalence remains unmeasured.","source_ids":["S1","S2","S3","S4"]},"externally_credible_adopter_or_authorizer":{"status":"UNCERTAIN","reason":"Mathlib and Stacks demonstrate credible maintainer authority, but neither requested this intervention and no named collaboration has offered a proof obligation or authorized a pilot.","source_ids":["S3","S4"]},"distinct_testable_incremental_claim":{"status":"YES","reason":"The ritual layer can be compared with a time-, ledger-, agenda-, and facilitation-matched plain review using ownership accuracy, seven-day recall, perceived pressure, and certification confusion.","source_ids":["S3","S5","S6"]},"bounded_next_evidence_step":{"status":"YES","reason":"A two-condition, single-site test involving one documented obligation per condition can be completed without changing theorem status and has explicit safety and efficacy falsifiers.","source_ids":["S5","S7"]},"no_unresolved_safety_or_authority_stop":{"status":"UNCERTAIN","reason":"The proposed safeguards are coherent, but a specific collaboration must assign technical authority and consent-monitor authority, assess confidentiality and employment consequences, and obtain a site-specific determination on human-subjects oversight before data collection.","source_ids":["S3","S4","S7"]},"credible_cost_scope_and_range":{"status":"YES","reason":"The work packages are bounded and the broad ranges are grounded in current official occupational wages with explicit labor, overhead, and infrastructure assumptions.","source_ids":["S8"]}},"next_evidence_step":"Recruit one willing long-lived collaboration and first document a real qualified or ambiguously owned dependency. After institutional research/privacy determination, run two 25-40 minute sessions on comparable obligations: the proposed marked renewal rite and a plain obligation-review control using the same dependency display, ledger fields, speaking opportunities, facilitator, duration, and follow-up. Counterbalance order if feasible. Pre-register ledger-entry accuracy and seven-day unaided status/owner recall as functional outcomes; perceived freedom to pass, pressure to speak or accept work, and mistaken belief that the session certified correctness as safety outcomes; and artifact delivery by existing deadlines as an exploratory outcome. Stop if anyone reports retaliation risk, surprise exposure, inaccessible participation, or certification confusion. Reject the incremental claim if the plain control is equal or better on ownership and recall, if passing is conspicuous or costly, if ledger entries are inaccurate, or if certification confusion is higher in the ritual condition.","blocking_evidence":["No direct evidence that proof obligations become socially unowned because of collaborator turnover at a specific project.","No named adopter or authorizer has expressed demand for, or agreed to host, the ritualized intervention.","No live evidence that participants can distinguish stewardship renewal from assent to theorem correctness.","No matched evidence that symbolic marking improves ownership accuracy or seven-day recall beyond a plain structured review.","No site-specific assessment of hierarchy, retaliation risk, confidentiality, accessibility, employment rules, data protection, or human-subjects review requirements.","No evidence that accepted obligations result in completed verification artifacts more often than under ordinary workflow."],"research_disposition":"PARTNERED_RESEARCH_PROGRAM","world_novelty_boundary":"The eight-source bounded search found established proof review, formalization, persistent dependency infrastructure, after-action review, and workplace group rituals, but no exact match for their proposed integration. This does not measure world novelty, patentability, freedom to operate, market size, or realized impact, and absence from this search must not be interpreted as absence from the world.","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_version":0,"controller_recommendation":{"action":"STOP_EMPIRICAL_RESEARCH_NEEDED","repairable":false,"material_progress_observed":true,"progress_targets":["Secure a named collaboration, technical authorizer, independent consent monitor, and one documented ambiguously owned proof obligation.","Obtain a written institutional determination covering human-subjects research, privacy, confidentiality, accessibility, and employment or authorship retaliation risks.","Pre-register a matched plain-review comparator, outcome definitions, scoring rules, missing-data handling, and stop/falsification thresholds.","Demonstrate in a live pilot that passing is genuinely low-cost and that participants do not mistake the session for mathematical certification.","Measure ledger accuracy, seven-day status/owner recall, perceived pressure, certification confusion, and artifact delivery against the control.","Publish negative and adverse findings and retire the ritual layer if it adds no benefit or increases pressure or false confidence."],"reason":"Bounded web research can establish the general proof-checking problem, adjacent practices, implementability, and a falsifiable contrast, but cannot determine turnover-specific prevalence at a host project, adopter willingness, lived coercion, certification confusion, or incremental performance. Those questions require proprietary project records, participant reports, and a live matched test."},"proposal_index":1}