{"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_proof_obligation_renewal_rite_v0","proposal_index":1,"version":0,"title":"Proof-Obligation Renewal Rite for Long-Lived Collaborative Theorems","problem":"A mathematical collaboration maintains a theorem whose proof is distributed across many lemmas, computations, conventions, and contributors. As membership changes, unresolved dependencies and qualified assumptions remain visible in documents but lose social ownership: participants can recite a general commitment to rigor while no one publicly renews responsibility for checking particular proof obligations. Ordinary status meetings transfer information but do not create a memorable, shared occasion for recognizing inherited work, permitting doubt, and reconnecting the theorem's asserted status to named verification actions.","actors":["Current proof authors","Maintainers of the theorem and dependency ledger","Independent proof reviewers","New or incoming collaborators","Contributors responsible for computational or case-checking components","Downstream mathematicians relying on the result","A rotating ritual facilitator with no authority to certify the theorem"],"observable_state":"The theorem dependency ledger contains at least one lemma, imported result, computation, or boundary case whose verification status is qualified, whose responsible checker is absent or ambiguous, or whose rationale is understood only by a departing contributor; meanwhile meeting records state a collective commitment to rigor without recording renewed acceptance, revision, or refusal of the corresponding obligations.","consequence":"Unresolved proof obligations can become normalized as inherited facts, newcomers may mistake social confidence for mathematical verification, and downstream work may proceed without a legible account of which claims remain conditional.","affected_objective":"Preserve the inspectability and accountable stewardship of a collaborative proof across participant turnover without treating collective confidence or ritual participation as evidence that the theorem is correct.","intervention":"Pilot a recurring, governed Proof-Obligation Renewal Rite at one natural proof milestone. Before the session, maintainers publish the theorem statement, dependency map, known qualifications, participation options, and a notice that the rite cannot certify correctness. A rotating facilitator opens with a reserved threshold mark and displays the current dependency map. Participants silently inspect one selected obligation, after which a plain marker circulates along a defined path; each recipient may pass, state a question, recognize completed checking, or offer a bounded verification task. The facilitator then invites participants to renew, revise, or decline only concrete stewardship commitments, never assent to the theorem itself. A named witness reads back owners, deliverables, deadlines, unresolved dissent, and resource needs. Closure returns every symbolic statement to an operational ledger entry. A short debrief records intended versus experienced meaning, exclusion, pressure, ambiguity, and owed follow-through. The group reviews the rite after the pilot and may adapt, pause, repair, or retire it independently of the theorem's mathematical status.","structural_mapping":[{"archetype_element":"Explicit and contestable meaning claim","domain_realization":"The rite means that proof stewardship must be periodically re-chosen and made inspectable; it explicitly does not mean that participants collectively believe, endorse, or certify the theorem."},{"archetype_element":"Participant and stakeholder boundary","domain_realization":"Authors, maintainers, reviewers, incoming collaborators, computational contributors, and affected downstream users are named separately, including people who rely on the theorem but do not attend."},{"archetype_element":"Legitimacy, consent, and exit","domain_realization":"Participation, speaking, accepting a task, and public recognition are independently optional; passing or leaving has no effect on authorship, employment, access, or mathematical standing."},{"archetype_element":"Recognizable cadence and trigger","domain_realization":"The practice occurs only at a declared milestone such as a major proof revision, maintainer handoff, or planned release, rather than at every routine meeting."},{"archetype_element":"Symbolic frame","domain_realization":"The displayed dependency map represents that a theorem is sustained by inspectable inferential relationships and inherited obligations, not by the prestige or confidence of its authors."},{"archetype_element":"Marked opening and sequence","domain_realization":"A reserved opening mark separates the bounded renewal period from ordinary technical discussion; the sequence is inspect, question or pass, offer or decline stewardship, witness obligations, and close into the ledger."},{"archetype_element":"Roles and rotating stewardship","domain_realization":"Facilitator, ledger keeper, obligation owners, independent witness, and consent monitor are distinct roles, with facilitation and record custody transferred on a scheduled rotation."},{"archetype_element":"Embodied but plural participation","domain_realization":"Participants may speak, write, sign, submit asynchronously, observe silently, or pass the circulating marker; no shared recitation of mathematical belief is required."},{"archetype_element":"Recognition and practical closure","domain_realization":"Completed checking is recognized only when its artifact is identified, while every renewed commitment closes as a named task, resource need, deadline, or explicitly unowned obligation."},{"archetype_element":"Emotional safety envelope","domain_realization":"The rite prohibits surprise attribution of mistakes, forced disclosure of uncertainty, and public interrogation; technical disputes move to ordinary review channels after the bounded session."},{"archetype_element":"Memory and handoff","domain_realization":"The dependency ledger stores provenance, qualifications, decisions, declined obligations, and stewardship rationale without treating any founder's interpretation as final."},{"archetype_element":"Drift, repair, and retirement","domain_realization":"Participant reports of coercion, rote performance, prestige capture, or divergence between spoken commitments and completed checks trigger independent review, modification, pause, or retirement."}],"mechanism_mapping":[{"mechanism_slug":"ritual_design_canvas","role":"Co-locates the rite's precise meaning, theorem boundary, sequence, participation paths, safeguards, ledger outputs, and retirement rule before the pilot.","counterfactual_removal":"Without the canvas, an attractive ceremony could be scripted before the group distinguishes proof stewardship from mathematical assent or specifies material follow-through."},{"mechanism_slug":"ritual_access_and_consent_review","role":"Applies pre-session vetoes to compulsory attendance, status-sensitive task acceptance, inaccessible participation, public exposure, recording, and retaliation for passing.","counterfactual_removal":"Without this review, visible refusal could become a loyalty or competence test, making apparent commitment uninterpretable."},{"mechanism_slug":"opening_marking_and_threshold_gesture","role":"Creates a brief, recognizable attentional boundary in which inherited proof obligations, rather than routine progress reports, are the shared object of attention.","counterfactual_removal":"Without the threshold, the activity could collapse into another agenda item and fail to establish a memorable renewal occasion distinct from information transfer."},{"mechanism_slug":"silence_reflection_and_lament_interval","role":"Provides a bounded, nonverbal interval for inspecting the selected dependency and acknowledging uncertainty or lost stewardship without demanding public performance.","counterfactual_removal":"Without the interval, fast or high-status speakers could define the apparent state of confidence before quieter participants examine or formulate doubts."},{"mechanism_slug":"symbolic_object_circulation","role":"Moves a plain turn marker through a declared path so opportunities to question, recognize, offer, or pass are publicly distributed rather than claimed by habitual speakers.","counterfactual_removal":"Without circulation, voice allocation would revert to informal status and the shared enactment of distributed stewardship would weaken."},{"mechanism_slug":"collective_commitment_renewal","role":"Lets participants periodically renew, revise, or decline specific checking and maintenance obligations, with each accepted obligation translated into a ledger entry.","counterfactual_removal":"Without periodic re-consent, tasks would remain stale assignments inherited from absent members or inferred from prior participation."},{"mechanism_slug":"witnessing_and_public_recognition","role":"A consented, independent witness acknowledges completed verification artifacts and reads back unresolved obligations and accepted commitments without declaring the theorem proven.","counterfactual_removal":"Without witnessed recognition and read-back, contributions and unresolved conditions could remain socially invisible, and closure could be mistaken for completion."},{"mechanism_slug":"after_ritual_meaning_debrief","role":"Immediately compares the intended meaning with experiences of pressure, exclusion, ambiguity, prestige effects, and the clarity of follow-through.","counterfactual_removal":"Without the debrief, organizers could infer legitimacy from smooth performance and carry unnoticed coercion or confusion into the next cycle."},{"mechanism_slug":"role_rotation_and_stewardship_rite","role":"Transfers facilitation, ledger custody, access credentials, and interpretive know-how together at a planned boundary.","counterfactual_removal":"Without actual transfer of authority and capability, founders could retain shadow control and the practice would remain vulnerable to their departure."},{"mechanism_slug":"ritual_drift_and_harm_audit","role":"Tests whether the rite has become rote, coercive, prestige-driven, detached from completed verification work, or falsely cited as evidence of correctness.","counterfactual_removal":"Without a skeptical audit, recognizable repetition could sanctify the collaboration's preferred account of rigor even when conduct contradicts it."}],"causal_chain":["Turnover and distributed proof structure leave some verification obligations socially unowned even when they remain textually visible.","A pre-announced, consent-reviewed milestone rite creates a bounded occasion distinct from routine reporting.","The marked opening and shared dependency map focus attention on the relationship between the theorem's asserted status and its supporting obligations.","Silent inspection plus visibly distributed, pass-permitted turns makes questions, uncertainty, recognition, and nonparticipation socially legible without requiring unanimity.","Periodic re-consent converts inherited expectations into accepted, revised, declined, or explicitly unowned stewardship obligations.","Witnessed closure translates symbolic renewal into ledger entries with artifacts, owners, resources, deadlines, qualifications, and unresolved dissent.","The immediate debrief and later harm audit compare the rite's meaning with participant experience and actual completion of verification work.","Adaptation, repair, or retirement prevents ritual continuity from outranking consent or mathematical evidence, while the ledger preserves proof stewardship across turnover."],"baseline":"Continue using ordinary research meetings, email requests, authorship conventions, and a technical dependency ledger. These can communicate proof status and assign tasks, but they do not provide a separately marked, recurring, consent-governed occasion for newcomers and incumbents to recognize inherited verification work, surface doubt, and re-choose obligations together.","nearest_rivals":["A proof assistant or machine-checked formalization that validates derivations but does not allocate or renew human stewardship of informal assumptions, translations, modeling choices, or unfinished formalization work.","Conventional peer review or an internal proof audit that evaluates correctness but is episodic, expert-centered, and not designed as a recurring, plural, consent-governed renewal of responsibility across turnover.","A responsibility matrix or issue tracker that assigns owners and deadlines but does not symbolically mark collective memory, recognition, refusal, witnessed handoff, or the difference between inherited and renewed obligation.","A research seminar or proof-reading meeting that supports technical discussion but may leave participation, consent, closure, memory, repair, and retirement implicit."],"remaining_contrastive_claim":"The proposal's distinctive functional claim is limited to joining a recurring symbolic enactment of distributed proof stewardship with costless refusal, witnessed conversion into concrete verification obligations, post-enactment meaning review, and an explicit retirement path. It does not claim to improve, replace, or constitute mathematical verification.","authority_safety":{"decision_authority":"The collaboration's existing proof-governance body may authorize or stop the pilot; technical owners retain authority over theorem statements and verification standards. An independent consent monitor may veto the rite for access or coercion concerns, but neither facilitator nor ritual participants may certify mathematical correctness by ceremony.","authorized_first_step":"Run one voluntary, non-recorded 25-minute pilot concerning one already-documented proof obligation with no publication or theorem-status decision attached; collect only the operational ledger output and anonymous immediate debrief responses.","excluded_actions":["Declaring the theorem, lemma, or computation valid because participants enacted or renewed commitments","Requiring attendance, speech, synchronized affirmation, task acceptance, or public explanation of refusal","Using silence, passing, absence, or criticism as evidence of disloyalty, incompetence, or reduced authorship standing","Publicly attributing a suspected error or incomplete check without the affected person's prior consent","Changing theorem status, authorship, employment, funding, access, or publication decisions during the pilot","Recording audio, video, names in feedback, or sensitive technical disclosures without separate explicit consent","Using the rite to substitute for line-by-line proof review, formal verification, replication, or correction"],"halt_rollback":"Stop immediately if any participant reports retaliation risk, compelled assent, surprise exposure, inaccessible participation, or confusion that the rite certifies correctness. Cancel pending ritual commitments, preserve only independently valid technical ledger facts approved by their owners, delete anonymous pilot feedback on request where identifiable, return all decisions to ordinary proof review, and either redesign under independent review or retire the rite with a written explanation."},"negative_tests":{"strongest_counterevidence":"If a plain, non-symbolic obligation-review meeting with the same ledger, speaking order, opt-out rules, and follow-up produces equally clear renewed ownership and equally durable handoff without the marked enactment being remembered or valued, the ritual layer adds no demonstrated function and may add pressure.","problem_falsifier":"The inferred problem is unsupported if inspection of the selected proof project finds no qualified or ambiguously owned dependencies, newcomers can accurately reconstruct the proof's verification status and rationale from existing records, and turnover has not interrupted stewardship of any obligation.","intervention_falsifier":"The intervention fails its initial test if participants cannot distinguish stewardship renewal from assent to correctness, passing is experienced as conspicuous or costly, ritual commitments do not become accurate ledger entries, or the pilot yields no more recall or ownership clarity than the matched ordinary review.","risks":["Collective enactment may manufacture apparent confidence in a theorem.","Visible passing may expose uncertainty or create professional pressure despite formal opt-out language.","Prestigious authors may capture the framing, witness role, or circulation path.","Symbolic closure may imply that an unresolved proof gap has been resolved.","Recognition may distort authorship or contribution credit.","The session may consume attention better spent on direct verification.","Repeated performance may become rote while ledger tasks remain incomplete.","The dependency map may omit disputed assumptions and make partial visibility look comprehensive."]},"next_evidence_step":"For one selected obligation, compare the voluntary ritual pilot with the collaboration's most recent ordinary obligation-review session using a bounded evidence sheet: anonymous immediate reports of perceived choice, clarity about what the rite did and did not establish, and pressure to speak; accuracy of the resulting owner-artifact-deadline ledger entries; and unaided recall of the obligation's status and owner after seven days. Inspect whether promised artifacts were delivered by their existing deadlines, without estimating a general effect size or changing theorem status.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Not assessed; exactly one proposal is in scope.","revision_record":{"parent_version":null,"progress_targets_addressed":["Produce one complete reverse-innovation candidate in mathematics","Preserve the archetype's governed cycle from symbolic meaning through practical follow-through, feedback, repair, and retirement","Bound authority and the first evidence step","State rivals, counterevidence, and falsifiers without novelty or effect-size claims"],"conceptual_changes":["Initial version; no parent proposal","Distinguished renewal of proof stewardship from mathematical assent or certification"],"operational_changes":["Specified a single-obligation, voluntary 25-minute pilot","Bound symbolic closure to an operational dependency ledger","Added independent consent veto, role rotation, halt, rollback, and retirement rules"],"evidence_changes":["Defined a matched ordinary-review comparison using consent, clarity, ledger accuracy, seven-day recall, and existing-deadline artifact completion","Kept prior-art status explicitly unsearched"],"claim_changes":["Limited the claim to the functional integration of ritualized stewardship renewal and governance","Excluded claims of novelty, prevalence, demand, effect size, or improved mathematical correctness"]}}