{"schema_version":1,"research_id":"eoa_inverse_innovation_exp06_external_evaluation_20260803","source_assessment_id":"ritualized_meaning_and_commitment_enactment__mathematics:P3:v0","cell_id":"ritualized_meaning_and_commitment_enactment__mathematics","search_queries":["site:ams.org mathematics research ethical guidelines errors correction attribution conjecture","mathematical conjecture disproved counterexample status open problem list archive","mathematics retraction correction policy journal official conjecture counterexample","ritual organizational change commitment empirical study synchrony coercion","site:aimath.org problem list update solved status corrections mathematics open problems","site:ams.org code ethics mathematical profession correct errors attribution","citations continue after retraction empirical study correction propagation scholarly record","mathematics failed conjecture partial results still useful counterexample research practice","American Institute Mathematics problem lists guidelines updating status solved problems","AIM workshop problem list maintainers open problems status solved","site:aimath.org \"problem lists\" mathematics","site:mathoverflow.net conjecture disproved still listed open problem","organization ritual funeral failed project postmortem practice","\"project funeral\" organizational ritual failure","research lab ritual retire failed hypothesis ceremony","mathematics ceremony disproved conjecture retirement","company \"funeral for a failed project\" ritual case study","organization \"funeral\" failed project ritual innovation","\"project funeral\" company failure learning ritual","\"funeral for\" \"failed project\" company","American Mathematical Society ethical guidelines correct errors mathematical results attribution official","site:ams.org/about-us/governance/policy-statements \"correct attribution\" mathematical","site:ams.org \"Code of Ethics\" mathematical profession corrections","London Mathematical Society ethical policy journals errors correction authors attribution","EEOC religious accommodation mandatory workplace ceremony ritual employee official guidance","EEOC Title VII religious practices workplace participation ceremonies official","university research group compelled speech ritual consent policy","ADA accessible meetings participation accommodations official guidance","\"Rituals decrease the neural response to performance failure\" DOI","Hobson Inzlicht rituals decrease neural response performance failure journal full text","rituals performance failure experimental study arbitrary ritual full text"],"sources":[{"source_id":"S1","title":"Putting math problems in proper order: AIM problem list tool for mathematics research","publisher":"American Institute of Mathematics","url":"https://aimath.org/news/problemlists/","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"2009-11-17","accessed_at":"2026-08-03","claims_supported":["Keeping track of long-lived mathematical problems and partial solutions is difficult even for experts.","AIM operates editable, expert-reviewed problem lists covering unsolved and previously unsolved problems.","AIM preserves permanent identifiers, version history, annotations, and archival continuity.","AIM and existing problem-list maintainers are identifiable potential adopters for accurate status and provenance workflows."]},{"source_id":"S2","title":"EMS Code of Practice for Mathematical Publication","publisher":"European Mathematical Society","url":"https://euromathsoc.org/code-of-practice","source_class":"OFFICIAL_GUIDANCE","publication_date":"2025-03-19","accessed_at":"2026-08-03","claims_supported":["Mathematicians should correct errors and attribution omissions promptly.","Authors remain responsible for the integrity and correctness of public mathematical material.","Editors should publish a correction or retraction when a mathematical statement or attribution is reported incorrect.","Correction authority belongs to ordinary authors, editors, referees, and publishers rather than a ceremonial facilitator."]},{"source_id":"S3","title":"Some instructive mathematical errors","publisher":"arXiv","url":"https://arxiv.org/abs/2106.07269","source_class":"PRIMARY_RESEARCH","publication_date":"2021-06-14","accessed_at":"2026-08-03","claims_supported":["Errors occur in professional mathematical literature and may remain undetected for years.","An incorrect refereed result produced further errors by a downstream author who relied on it.","Correcting mathematical errors can preserve or generate useful mathematics.","The paper covers false conjectures and results announced outside formal publication, supporting a scope broader than journal retraction alone."]},{"source_id":"S4","title":"Self-correction in science: The effect of retraction on the frequency of citations","publisher":"PLOS ONE","url":"https://journals.plos.org/plosone/article/file?id=10.1371%2Fjournal.pone.0277814&type=printable","source_class":"PRIMARY_RESEARCH","publication_date":"2022-12-07","accessed_at":"2026-08-03","claims_supported":["In matched samples of more than 3,000 retracted and 3,000 control papers, retraction reduced but did not eliminate later citation.","Retracted papers averaged about two citations per year after retraction, demonstrating informational afterlife after formal status change.","The authors distinguish inadvertent error from misconduct and argue that self-correction should not automatically carry stigma.","This is cross-disciplinary evidence and does not measure conjecture-status propagation specifically in mathematics."]},{"source_id":"S5","title":"Postmortem Culture: Learning from Failure","publisher":"Google","url":"https://sre.google/workbook/postmortem-culture/","source_class":"COMMERCIAL_FIRST_PARTY","publication_date":"2018","accessed_at":"2026-08-03","claims_supported":["Google documents a repeatable blameless-postmortem practice linking shared review, written records, action, and organizational learning.","The practice can start with a basic procedure and be tuned after reflection.","Postmortems are a close workflow analogue for learning, blame prevention, documentation, and assigned follow-through."]},{"source_id":"S6","title":"Planet Blue Student Leaders Annual Report 2021–22","publisher":"University of Michigan","url":"https://planetblue.umich.edu/campus/uploads/pbsl-annual-report-2021-22.pdf","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"2022","accessed_at":"2026-08-03","claims_supported":["A university program used a theatrical “Funeral for a failed project” workshop.","The workshop combined postmortem analysis, memorial performance, preservation of worthwhile aspects, empathy for organizers and affected people, and restorative reflection.","This is substantial direct prior art for ritualized project retirement, although it is pedagogical and not a mathematical-status workflow."]},{"source_id":"S7","title":"Rituals decrease the neural response to performance failure","publisher":"PeerJ","url":"https://peerj.com/articles/3363.pdf","source_class":"PRIMARY_RESEARCH","publication_date":"2017-05-30","accessed_at":"2026-08-03","claims_supported":["A preregistered experiment provides preliminary causal evidence that arbitrary ritual can alter neural performance monitoring after failure.","The evidence supports only a possible individual regulatory mechanism, not group record correction, consent, recall, or mathematical workflow outcomes.","Dampening response to failure could be beneficial for stigma but could also reduce attention to error, so the direction of operational effect remains uncertain."]},{"source_id":"S8","title":"Section 12: Religious Discrimination","publisher":"U.S. Equal Employment Opportunity Commission","url":"https://www.eeoc.gov/laws/guidance/section-12-religious-discrimination","source_class":"GOVERNMENT_OR_REGULATOR","publication_date":"2021-01-15","accessed_at":"2026-08-03","claims_supported":["U.S. employers may need to excuse employees from workplace celebrations, initiatives, meditation, or similar participation that conflicts with sincerely held religious beliefs.","Conditioning advancement on participation in religious practice can create discrimination and harassment liability.","A secularly intended ritual can still require accommodation if an employee experiences a religious conflict.","The guidance supports genuine alternatives and nonretaliation; jurisdiction-specific legal review remains necessary outside its U.S. employment scope."]}],"problem_evidence":{"support":"MODERATE","rationale":"Mathematics-specific sources establish that problem-state tracking is difficult, errors can persist for years, incorrect results can generate downstream errors, and corrections are an explicit professional obligation. Cross-disciplinary citation evidence confirms that formal invalidation does not fully terminate downstream use. None of the sources measures how often an already-disproved or withdrawn conjecture remains active in research-group slides, student projects, or repositories, so the proposal's exact prevalence and burden remain unverified.","source_ids":["S1","S2","S3","S4"]},"stakeholder_evidence":{"support":"MODERATE","rationale":"AIM is an identifiable operator and potential adopter of versioned problem-status infrastructure and explicitly solicits existing problem-list maintainers. EMS identifies authors, editors, referees, and publishers as authorities responsible for correction. These sources express demand for accurate status, provenance, and correction, but no mathematics organization expresses demand for a symbolic retirement observance itself.","source_ids":["S1","S2"]},"prior_art":{"proximity":"SUBSTANTIAL_COLLISION","closest_analogues":[{"name":"AIM Problem Lists","similarity":"Versioned, permanent, expert-reviewed records track current and previously unsolved mathematical problems, related work, commentary, and historical change.","remaining_difference":"AIM provides the core informational and archival workflow but not a consent-governed, symbolically marked group transition, recognition session, or emotional-safety protocol.","source_ids":["S1"]},{"name":"Mathematical correction and retraction practice","similarity":"The EMS code assigns responsibility and authority for correcting false mathematical statements and attribution errors through ordinary publication governance.","remaining_difference":"It applies principally to disseminated mathematical work and does not prescribe a research-group handoff for informal artifacts, partial results, or social closure.","source_ids":["S2"]},{"name":"Blameless postmortem practice","similarity":"Google's practice combines a bounded review, shared written account, blame avoidance, action items, dissemination, and iterative improvement after failure.","remaining_difference":"It analyzes operational incidents rather than an independently adjudicated mathematical claim and lacks the proposal's exact-status archive movement and reopening semantics.","source_ids":["S5"]},{"name":"Funeral for a failed project","similarity":"The University of Michigan example directly uses funeral roles, memorial performance, postmortem analysis, empathy, and preservation of worthwhile residues from a failed project.","remaining_difference":"It is a pedagogical workshop, not a recurring mathematical correction protocol with technical witnesses, exact conjecture statements, downstream citation repair, independent opt-outs, and transparent mathematical reopening.","source_ids":["S6"]}],"distinctive_claim_remaining":"After ordinary mathematical review has independently settled a conjecture's status, adding a brief, opt-in, math-specific symbolic handoff to an otherwise identical correction checklist will improve 14-day completion of required artifact updates and downstream recall of both the status and preserved mathematical residue, without increasing reported coercion, blame, or false-finality signals. A pilot should treat less than a 15-percentage-point completion gain, no recall gain, or more than a 5-percentage-point increase in any safety signal as failure of the ritual increment. These thresholds are decision rules, not evidence-based effect estimates.","confidence":"HIGH"},"implementation_evidence":{"support":"MODERATE","rationale":"The necessary technology is routine: a versioned record, archived counterexample, affected-artifact inventory, task owners, notices, and survey forms. AIM demonstrates durable mathematical problem records, while Google demonstrates repeatable blameless reviews and Michigan demonstrates that a project-funeral workshop can be run institutionally. PeerJ supplies only preliminary individual-level mechanism evidence. No source demonstrates that the combined ritual improves mathematical correction over a checklist, and implementation must preserve technical-authority separation, accessibility, religious accommodation, privacy, and nonretaliatory refusal.","source_ids":["S1","S5","S6","S7","S8"]},"scores":{"meaningful_impact":{"score":3,"rationale":"Accurate status and dependency correction could prevent wasted work and preserve useful mathematics, but the frequency, severity, and affected population for this exact problem are unknown.","source_ids":["S1","S3","S4"]},"stakeholder_pull":{"score":2,"rationale":"Professional bodies and problem-list operators express need for correction and current records, but no identified stakeholder requests the ritual layer.","source_ids":["S1","S2"]},"incremental_advantage":{"score":2,"rationale":"The proposed increment may improve salience, memory, and dignity, but checklists, problem-list versioning, corrections, blameless postmortems, and failed-project funerals already cover most functions; no comparative outcome evidence supports added ritual value.","source_ids":["S1","S2","S5","S6","S7"]},"distinctiveness_plausibility":{"score":2,"rationale":"The exact combination of mathematical adjudication boundaries, archival movement, consent, residue handoff, and reopening is plausibly distinctive, but its components substantially collide with established adjacent practices.","source_ids":["S1","S2","S5","S6"]},"technical_implementability":{"score":5,"rationale":"A pilot requires ordinary version control, documents, forms, task tracking, and a short facilitated session; no new scientific or software capability is needed.","source_ids":["S1","S5","S6"]},"adoption_authority_feasibility":{"score":4,"rationale":"Authors, project leaders, repository maintainers, and editors can authorize bounded correction workflows, while the facilitator is properly denied power over mathematical truth. Institutional employment and accommodation rules must still be observed.","source_ids":["S1","S2","S8"]},"evidence_readiness":{"score":3,"rationale":"Artifact completion, status recall, residue recall, and safety signals are measurable with a checklist-only comparator, but prevalence data, a committed partner, and direct baseline observations are absent.","source_ids":["S1","S3","S4"]},"safety_net_benefit":{"score":3,"rationale":"Explicit attribution, preserved residue, opt-outs, and reopening could reduce erasure and premature closure, but ritual could also stigmatize authors or dampen attention to error unless independently monitored.","source_ids":["S2","S7","S8"]},"scalability":{"score":3,"rationale":"Templates and archives are inexpensive to reproduce, but eligible retirements are episodic, local authority differs, and cultural acceptance of ceremonial framing is unlikely to be uniform.","source_ids":["S1","S5","S6","S8"]}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Design and preregister one comparative tabletop study with 24–40 mathematicians, construct a sandbox conjecture archive and dependency set, facilitate checklist-only and checklist-plus-ritual conditions, analyze outcomes, and conduct an independent safety review.","confidence":"LOW","assumptions":["80–180 hours of research, facilitation, technical setup, recruitment, analysis, and reporting at blended 2026 resource-equivalent rates","Participant honoraria or compensated staff time","No custom software, travel, or publication charge","The band is bottom-up and not derived from published prices"],"source_ids":["S5","S6"]},"initial_deployment_startup":{"band_2026_usd":"10K_TO_50K","scope":"Adapt templates to one mathematics program, map authority and artifacts, obtain institutional legal/accessibility review, configure versioned archives and notices, train a facilitator and consent monitor, and rehearse halt/reopening procedures.","confidence":"LOW","assumptions":["100–250 staff hours across mathematical leadership, archive administration, facilitation, accessibility, and counsel","Existing repository, survey, and task-management systems are reused","No public communications campaign or integration with multiple publishers"],"source_ids":["S1","S2","S5","S8"]},"operational_launch":{"band_2026_usd":"UNDER_10K","scope":"Run one 30-minute internal observance for one already-settled nonpublic conjecture, including preparation, accessible alternatives, technical witnessing, task assignment, debrief, and 14-day verification.","confidence":"MODERATE","assumptions":["25–60 total labor hours including participant time","No honoraria, travel, venue rental, or new software","The technical verdict and counterexample archive are complete before launch","No employment, funding, authorship, or publication decision is attached"],"source_ids":["S5","S6","S8"]},"annual_recurring":{"band_2026_usd":"10K_TO_50K","scope":"Maintain templates and archives, run approximately four to eight eligible handoffs, verify downstream corrections, provide accommodations, and conduct one annual drift-and-harm audit.","confidence":"LOW","assumptions":["40–120 staff hours per year plus participant time","Incidence of eligible conjecture retirements is highly uncertain","Existing institutional systems host records and surveys","The band excludes mathematical review that would occur regardless of the intervention"],"source_ids":["S1","S5","S6"]}},"verified_pipeline_gates":{"externally_supported_problem":{"status":"YES","reason":"Mathematics-specific evidence shows difficult problem-state maintenance, delayed error discovery, and downstream reliance on incorrect results; broader empirical evidence shows that formal invalidation does not fully stop later use.","source_ids":["S1","S3","S4"]},"externally_credible_adopter_or_authorizer":{"status":"YES","reason":"AIM is an identifiable operator of expert-governed, versioned problem lists and invites existing list maintainers to use its tooling; EMS identifies authors, editors, and publishers as legitimate correction authorities. This verifies credible authority and workflow need, not willingness to adopt a ceremony.","source_ids":["S1","S2"]},"distinct_testable_incremental_claim":{"status":"YES","reason":"The ritual layer can be compared against the same briefing, archive, and correction checklist using completion, recall, and safety outcomes with prespecified failure thresholds.","source_ids":["S1","S5","S6","S7"]},"bounded_next_evidence_step":{"status":"YES","reason":"A sandboxed, preregistered two-condition tabletop study can be completed without changing any live mathematical status and can directly falsify added operational value or reveal safety harms.","source_ids":["S5","S6","S8"]},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"No inherent stop remains if the mathematical verdict is settled outside the observance, participation and recognition are optional, accommodations are available, data are minimized, and the consent monitor can halt the session. Failure to implement these conditions would reopen the gate.","source_ids":["S2","S8"]},"credible_cost_scope_and_range":{"status":"YES","reason":"All four estimates identify included work, labor assumptions, reused infrastructure, and exclusions. Confidence is appropriately low where no external unit-cost evidence exists.","source_ids":["S1","S5","S6"]}},"next_evidence_step":"With AIM or one willing mathematics research program, preregister a sandboxed two-arm tabletop study using the same independently validated false-conjecture packet, five affected artifacts, counterexample deposit, downstream notices, and surviving-result inventory. Randomly assign 24–40 participants in small groups to (A) a plain technical briefing plus correction checklist or (B) the identical briefing and checklist plus the proposed opt-in symbolic handoff. Blind assessors should score artifact accuracy and completion immediately and at 14 days; downstream-role participants should state the status, decisive reason, one preserved result, and whether reopening remains allowed. Collect anonymous coercion, blame, exposure, religious-conflict, and false-finality reports. Stop development if condition B improves completion by less than 15 percentage points, produces no recall improvement, creates any technical-status confusion, or raises any safety signal by more than 5 percentage points. Only a favorable tabletop result should authorize one live, nonpublic pilot.","blocking_evidence":["No direct prevalence estimate for settled conjectures remaining active in mathematics-group artifacts or downstream plans.","No mathematics adopter has expressed demand for a symbolic retirement layer or committed to a pilot.","No head-to-head evidence shows that the ritual adds value over a versioned checklist and technical briefing.","No live evidence establishes that junior contributors can refuse without reputational or supervisory consequences.","The frequency of eligible events and resulting annual operating burden are unknown.","Accessibility, privacy, employment, and religious-accommodation review remains institution- and jurisdiction-specific."],"research_disposition":"PARTNERED_RESEARCH_PROGRAM","world_novelty_boundary":"The search found substantial adjacent and component-level prior art, including mathematical correction standards, versioned problem lists, blameless postmortems, and an institutional funeral for a failed project. It did not establish a published mathematics-specific conjecture-retirement ceremony with the proposal's complete authority, consent, archival, dependency-correction, and reopening structure. World novelty, patentability, freedom to operate, market size, and realized impact remain unmeasured.","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 mathematics-program partner and written authorization for a sandbox comparison.","Measure baseline prevalence through a bounded inventory of settled conjectures and maintained artifacts.","Run the checklist-only versus checklist-plus-ritual comparison with identical technical content and blinded outcome scoring.","Demonstrate improved completion and recall without coercion, blame, religious conflict, or false finality.","Document nonretaliatory refusal for students and junior collaborators and validate halt/reopening procedures.","Differentiate the intervention operationally from AIM-style versioning, ordinary corrections, blameless postmortems, and failed-project funerals.","Replace low-confidence cost assumptions with observed labor and accommodation data from the study."],"reason":"Web research establishes a credible correction and status-propagation problem, identifiable authorities, strong adjacent prior art, technical feasibility, and a bounded comparative test. It does not establish the ritual increment's benefit or safety in mathematical research groups. Answering that question requires participant fieldwork and controlled live or tabletop testing rather than additional bounded web search."},"proposal_index":3}