{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"ritualized_meaning_and_commitment_enactment__mathematics","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"math_conjecture_retirement_handoff_v0","proposal_index":3,"version":0,"title":"Conjecture Retirement and Counterexample Handoff","problem":"After ordinary mathematical review establishes that a research program's conjecture is false or no longer defensible, the formal status change may not become a shared, durable transition. Slides, informal notes, student projects, and collaborators' plans can continue treating the conjecture as active; contributors may experience withdrawal as erasure of their work; and the counterexample, useful partial results, and abandoned approaches may not enter collective memory. A database label or announcement changes information but does not necessarily renew the group's commitment to correct the record, recognize contributions without preserving a false claim, and carry reusable mathematical residue forward.","actors":["Authors and sponsors of the conjecture","Discoverers and checkers of the counterexample","Researchers who developed partial results or failed approaches","Students and junior collaborators working under the conjecture","Maintainers of project repositories and public problem lists","Downstream collaborators whose work cites or assumes the conjecture","A rotating facilitator and an independent consent monitor"],"observable_state":"A conjecture already classified as false or withdrawn through ordinary technical review remains labeled active in at least one maintained artifact, continues to appear without qualification in a planned talk or project, lacks an archived and citable counterexample record, or has no named disposition for partial results and dependent work.","consequence":"Researchers may repeat invalidated approaches, allocate work under an obsolete premise, cite an inaccurate status, lose reusable results, or interpret correction as repudiation of contributors rather than revision of a mathematical claim.","affected_objective":"Make the post-review retirement of a conjecture socially legible and operationally complete while preserving counterexample provenance, reusable mathematics, accurate downstream records, contributor dignity, and permission to reopen the question if later evidence warrants it.","intervention":"Establish an event-triggered Conjecture Retirement and Counterexample Handoff used only after an authorized technical process has independently settled the conjecture's current status. Before each observance, stewards publish the exact statement, status decision, counterexample or withdrawal basis, affected artifacts, participation alternatives, recognition permissions, and required record changes. A rotating facilitator opens a bounded session with a reserved mark, states that the ceremony neither decides nor strengthens the mathematical verdict, and retells the conjecture's provenance with room for correction. A named technical witness presents the already-reviewed counterexample or reason for withdrawal. After a timed, optional silence, a plain question card circulates; participants may identify a result, method, warning, dependency, or unresolved objection to preserve, contribute privately or asynchronously, or pass. With no required unison response, the conjecture record moves visibly from an active display to a historical archive marked with its exact status and reason. Contributors and counterexample checkers who consent are recognized for specified work. Closure assigns repository edits, citation corrections, downstream notices, archive deposits, and stewardship of surviving questions to named owners and deadlines. An immediate debrief and a later drift audit determine whether the practice should be retained, repaired, or retired.","structural_mapping":[{"archetype_element":"Explicit and contestable meaning claim","domain_realization":"The observance enacts that mathematical claims remain answerable to counterevidence while work performed under a false conjecture can retain value; it does not demand agreement about the conjecture's historical importance or contributors' motives."},{"archetype_element":"Participant and stakeholder boundary","domain_realization":"Conjecture authors, counterexample discoverers, partial-result contributors, junior researchers, repository maintainers, and downstream users are separately identified, including affected people who do not attend."},{"archetype_element":"Legitimacy, consent, and exit","domain_realization":"Only an existing technical authority can set the mathematical status. Attendance, speech, recognition, silence, object handling, and disclosure are independently optional and have no effect on credit, employment, funding, access, or standing."},{"archetype_element":"Ritual time, place, and cadence","domain_realization":"The observance is triggered when the program completes an authorized retirement or withdrawal decision and recurs under the same governed form for later eligible conjectures."},{"archetype_element":"Symbolic frame and shared narrative","domain_realization":"Moving the exact conjecture statement from an active display to a historical archive represents release from an obsolete research commitment without deleting provenance or mathematical residue."},{"archetype_element":"Ritual script and sequence","domain_realization":"The recognizable sequence is threshold, status boundary, provenance account, witnessed counterevidence, bounded reflection, plural residue collection, archival movement, recognition, operational commitments, and closure."},{"archetype_element":"Role, witness, and facilitation structure","domain_realization":"Technical status authority, facilitator, counterexample witness, consent monitor, archive steward, affected contributor, and downstream notifier have distinct roles; facilitation and archive custody rotate."},{"archetype_element":"Marked object, space, or gesture","domain_realization":"A removable copy of the exact conjecture statement and a reversible active-to-historical placement distinguish the occasion without making the document intrinsically sacred."},{"archetype_element":"Attention and participation path","domain_realization":"A timed silence and circulating question card distribute attention among the verdict, retained results, counterexample provenance, and unresolved objections while allowing passing and asynchronous contribution."},{"archetype_element":"Recognition and practical closure","domain_realization":"Recognition names specific contributions rather than celebrating agreement, and closure converts the transition into repository changes, notices, deposits, owners, and deadlines."},{"archetype_element":"Plural meaning and emotional safety","domain_realization":"Participants may regard the retirement as loss, correction, relief, or routine maintenance; no emotional display, confession, apology, praise, or public account of failed work is required."},{"archetype_element":"Memory and intergenerational handoff","domain_realization":"The archive preserves the conjecture's versions, provenance, decisive counterevidence, partial results, failed approaches contributors choose to record, status changes, and surviving questions."},{"archetype_element":"Renewal and drift signal","domain_realization":"Each observance renews the program's commitments to corrigibility, accurate status reporting, and preservation of reusable work; debriefs test whether the enactment instead produces blame, mythmaking, or empty closure."},{"archetype_element":"Repair and retirement path","domain_realization":"Incorrect attribution, premature closure, coerced participation, or a later mathematical reversal can trigger correction, reopening, apology, redesign, pause, or retirement of the observance itself."}],"mechanism_mapping":[{"mechanism_slug":"ritual_design_canvas","role":"Co-locates the precise meaning claim, technical precondition, affected parties, provenance, sequence, recognition rules, operational changes, evidence, and exit path before an observance is authorized.","counterfactual_removal":"Without the canvas, organizers could script emotional closure before separating the mathematical verdict from the social and archival work that follows."},{"mechanism_slug":"ritual_access_and_consent_review","role":"Applies vetoes to surprise attribution, compulsory attendance, public exposure of failed work, inaccessible participation, recording pressure, or retaliation for dissent and absence.","counterfactual_removal":"Without independent consent review, the observance could become a compelled confession or reputational punishment for conjecture sponsors."},{"mechanism_slug":"opening_marking_and_threshold_gesture","role":"Creates a bounded transition from ordinary research discussion to shared attention on correction, memory, and release of inherited commitments.","counterfactual_removal":"Without the threshold, retirement tasks may fragment across routine administration and fail to become a common, memorable change in the program's status."},{"mechanism_slug":"story_myth_or_origin_reenactment","role":"Reconstructs why the conjecture was posed, how it changed, and what work it generated while explicitly allowing corrections and competing interpretations.","counterfactual_removal":"Without a provenance account, retirement may flatten a defensible research history into a story of obvious error or erase contributions that remain mathematically useful."},{"mechanism_slug":"witnessing_and_public_recognition","role":"A credible technical witness presents the already-reviewed basis for retirement, while consented recognition names particular contributions and counterexample work without manufacturing loyalty.","counterfactual_removal":"Without witnessed truth and bounded recognition, the event could become either an unsupported announcement or a generalized tribute that obscures what mathematically changed."},{"mechanism_slug":"silence_reflection_and_lament_interval","role":"Provides a disclosed, time-limited interval in which participants may privately register loss, correction, uncertainty, or relief without performing an emotion or endorsing a shared interpretation.","counterfactual_removal":"Without the interval, immediate technical or celebratory speech may crowd out divergent experiences and considered identification of what should be preserved."},{"mechanism_slug":"symbolic_object_circulation","role":"A plain question card distributes opportunities to name retained results, dependencies, cautions, or objections, with pass and private-submission options.","counterfactual_removal":"Without a protected distribution path, senior sponsors or counterexample discoverers could dominate the account of what the conjecture leaves behind."},{"mechanism_slug":"collective_commitment_renewal","role":"Participants may accept, revise, or decline concrete obligations to correct records, notify dependents, archive evidence, or steward surviving questions.","counterfactual_removal":"Without periodic re-consent tied to specific actions, the ceremony could announce corrigibility while leaving inaccurate artifacts and abandoned dependencies unchanged."},{"mechanism_slug":"ritual_retirement_or_repair_ceremony","role":"Discharges the obsolete shared practice of treating the conjecture as active, releases its status marker, preserves memory, and transfers live obligations instead of simply deleting the claim.","counterfactual_removal":"Without explicit discharge and transfer, the conjecture may retain a social half-life or disappear together with valuable provenance and unfinished obligations."},{"mechanism_slug":"after_ritual_meaning_debrief","role":"Immediately compares intended correction and preservation with experienced blame, coercion, ambiguity, exclusion, premature closure, and clarity of follow-through.","counterfactual_removal":"Without the debrief, a smooth session could be misread as legitimate closure despite harm or confusion among affected contributors."},{"mechanism_slug":"ritual_drift_and_harm_audit","role":"Checks whether observances have become prestige theater, scapegoating, forced consensus, inaccurate historical reconstruction, or substitutes for record correction.","counterfactual_removal":"Without skeptical review, the practice could protect the program's preferred story while leaving mathematical records and power relations unexamined."},{"mechanism_slug":"role_rotation_and_stewardship_rite","role":"Transfers facilitation, archive access, notification authority, and tacit knowledge of the process together on a declared cadence.","counterfactual_removal":"Without actual rotation, conjecture sponsors or a permanent founder could control interpretation, recognition, and which retirements receive a legitimate ending."}],"causal_chain":["Ordinary technical review changes a conjecture's formal status, but distributed artifacts, research identities, dependencies, and memories do not update automatically.","A consent-reviewed, event-triggered observance creates a bounded occasion whose purpose is correction, preservation, and release rather than adjudication.","The exact statement, provenance account, and witnessed counterevidence establish a common and contestable account of what changed.","Protected reflection and distributed, pass-permitted residue collection separate the conjecture's failure from the worth of contributors and surface results, warnings, and objections worth preserving.","Visible movement from active to historical status makes release of the former research commitment socially legible without erasing the claim.","Consented recognition preserves contribution while refusing to treat prestige or effort as support for mathematical truth.","Closure converts the symbolic transition into owned archive edits, citation corrections, downstream notices, counterexample deposits, and stewardship of surviving questions.","Debrief, audit, repair, and reopening rules keep mathematical evidence, consent, and accurate records authoritative over ceremonial finality."],"baseline":"Announce the counterexample or withdrawal in a meeting or email, change a repository label, and rely on individual contributors to update their own talks, notes, and projects. This can transmit the verdict but may leave recognition, shared memory, affected dependencies, practical follow-through, divergent experience, and legitimate closure ungoverned.","nearest_rivals":["A repository deprecation or withdrawal checklist that can complete status edits and notifications but does not provide a shared, symbolically marked occasion for recognition, memory transfer, plural response, or release of inherited commitments.","A technical counterexample seminar that explains why the conjecture fails but need not govern consent, contributor recognition, downstream correction, archival handoff, or retirement of the conjecture's social role.","A project postmortem that analyzes decisions and lessons but may frame the conjecture as managerial failure rather than enact a recurring, corrigible mathematical commitment to truth over prestige.","A journal correction, erratum, or retraction process that governs a publication record but does not cover unpublished conjectures, research-group identity, preserved dead ends, or the broader network of informal artifacts.","A version-controlled dependency inventory that locates affected materials but does not itself make the status transition collectively interpretable or protect contributors from erasure and blame."],"remaining_contrastive_claim":"The proposal's limited functional claim is that an already-settled mathematical retirement can be joined to a recurring, consent-governed symbolic discharge that preserves provenance, recognizes work, transfers surviving obligations, and verifies operational correction. It does not claim that ceremony determines truth, resolves technical disagreement, or makes every conjecture worthy of commemoration.","authority_safety":{"decision_authority":"The authors, repository maintainers, editors, or other predesignated technical authority determine conjecture status through ordinary mathematical review. The ritual facilitator can execute or halt the observance but cannot declare a conjecture false, withdrawn, restored, or historically important. The consent monitor may veto public participation or recognition practices.","authorized_first_step":"Pilot one 30-minute internal observance for a nonpublic conjecture whose false or withdrawn status, exact reason, and counterexample record have already been approved through the group's ordinary technical process; attach no funding, hiring, authorship, publication, or project-termination decision to the pilot.","excluded_actions":["Using the observance to decide or strengthen the conjecture's mathematical status","Retiring a conjecture while its authorized technical status remains unresolved","Compelling attendance, speech, silence, object handling, emotional display, apology, recognition, or task acceptance","Inferring blame, incompetence, loyalty, agreement, or credit from participation or refusal","Changing authorship, employment, funding, supervision, or publication standing during the observance","Publicly naming failed approaches, personal reactions, or contributors without specific prior consent","Declaring all dependent work false or valueless without item-specific mathematical review","Deleting the original conjecture, counterexample, objections, or provenance as a form of closure","Substituting the ceremony for repository correction, citation repair, downstream notice, or technical documentation"],"halt_rollback":"Halt if the technical status is credibly disputed, the displayed counterexample or history is inaccurate, an affected person reports pressure or surprise exposure, or participants treat closure as authority over future mathematics. Return the statement to a neutral pending display without altering its independently authorized formal status, suspend public recognition and notices, correct or withdraw inaccurate records, preserve objections, cancel unaccepted ritual commitments, and resume only after ordinary technical and consent review. A later valid reopening updates the archive transparently rather than erasing the retirement record."},"negative_tests":{"strongest_counterevidence":"If a plain status-change checklist and technical briefing complete the same artifact corrections, preserve the same reusable results and provenance, produce equally accurate downstream understanding, and are preferred by affected contributors because the symbolic observance adds pressure or no useful meaning, the ritual layer should be retired.","problem_falsifier":"The inferred problem is unsupported for the selected program if every maintained artifact already reflects the authorized status, downstream users can identify the counterexample and its implications, reusable results and failed approaches are preserved with consent, and contributors report no ambiguity about closure or recognition.","intervention_falsifier":"The intervention fails its bounded test if participants confuse ceremony with mathematical adjudication, experience retirement as blame or coerced finality, cannot accurately state the conjecture's post-review status and surviving results, or assigned record corrections and notices remain incomplete.","risks":["Ceremonial finality may discourage legitimate attempts to repair or reformulate the conjecture.","The event may stigmatize conjecture authors or turn correction into public blame.","A compelling origin story may rewrite contested history around senior participants.","Recognition may undercredit counterexample discoverers, junior contributors, or unpublished labor.","Symbolic movement may imply that all dependent results fail together.","The observance may elevate a routine correction into unnecessary emotional exposure.","Prestigious sponsors may control which residues are preserved or which objections are heard.","Repository edits may lag behind the ceremony, producing symbolic closure without material correction.","Reopening may be socially resisted because retirement was publicly enacted."]},"next_evidence_step":"For the single internal pilot, inventory a bounded set of maintained artifacts before the observance: the conjecture record, counterexample deposit, one project list, one planned presentation, and notices to named downstream collaborators. Within fourteen days, check whether each required status correction, provenance deposit, notification, and surviving-question assignment was completed. Collect anonymous immediate reports about consent, blame, clarity, finality, and what participants believed the observance established, then ask affected collaborators to state the conjecture's current status, decisive reason, and one preserved result or open question. Use only these pilot-specific observations to keep, adapt, or retire the practice.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Proposal 1 renews human ownership of unresolved verification obligations supporting an extant collaborative theorem; proposal 3 begins only after ordinary review has already ended an active conjecture and addresses its lingering social status, dispersed records, contributor recognition, and mathematical residue. Its causal path is symbolic discharge plus archival and downstream correction, not renewed proof-checking responsibility. Proposal 2 helps students stop importing conclusions across axiom systems by enacting a change of formal context during instruction; proposal 3 concerns a research program's response to counterevidence against one conjecture, uses provenance, witnessed retirement, and obligation transfer rather than premise replacement, and has no curricular or learning-assessment dependency. The proposal is independently adoptable as a research-program correction and memory practice without the theorem ledger of proposal 1 or the comparative-geometry course of proposal 2.","revision_record":{"parent_version":null,"progress_targets_addressed":["Generate one complete candidate at proposal index 3","Address a problem materially different from proposals 1 and 2","Use an independently adoptable intervention and causal path","Preserve consent, meaning, practical follow-through, memory, review, repair, and retirement","Provide rivals, authority limits, safeguards, falsifiers, and bounded first evidence"],"conceptual_changes":["Initial version; no parent proposal","Centered the candidate on the social and archival half-life of an already-retired conjecture","Separated technical adjudication from ritualized correction, recognition, memory transfer, and release"],"operational_changes":["Specified an event-triggered 30-minute internal pilot after completed technical review","Bound closure to artifact corrections, counterexample deposit, downstream notices, and surviving-question ownership","Added consented recognition, neutral rollback, transparent reopening, rotating stewardship, and retirement rules"],"evidence_changes":["Defined a pre-observance artifact inventory and fourteen-day completion check","Added anonymous measures of consent, blame, clarity, and false finality plus bounded collaborator recall","Kept prior-art status explicitly unsearched"],"claim_changes":["Limited the claim to governed symbolic discharge and operational handoff after a settled retirement","Excluded claims of novelty, prevalence, demand, effect size, or truth determination by ceremony"]}}