{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"ritualized_meaning_and_commitment_enactment__mathematics","portfolio_valid":true,"proposal_assessments":[{"proposal_index":1,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally specifies the trigger, roles, consent paths, marked sequence, ledger-bound closure, review, rollback, and bounded evidence test. It faithfully converts abstract proof-stewardship obligations into a recurring symbolic enactment while explicitly preventing ceremony from certifying correctness."},{"proposal_index":2,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Provides an executable axiom-transition ritual with multimodal refusal, reversible symbolic media, witnessed classification, instructional follow-through, correction, and retirement. Its causal target is students' context-insensitive reasoning, addressed through enacted premise replacement and salient dependency change."},{"proposal_index":3,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Fully separates prior technical adjudication from the governed retirement observance and specifies provenance, consented recognition, archival transfer, downstream correction, reopening, repair, and evidence checks. Symbolic discharge makes an already-settled status change socially durable without claiming authority over truth."},{"proposal_index":4,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally defines independent facilitation, student-controlled participation, multiple legitimate paths, reciprocal support commitments, confidential records, rollback, audit, and a bounded pilot. It faithfully ritualizes periodic re-consent to a research relationship while preserving ordinary mathematical and degree authority."}],"pairwise_assessments":[{"proposal_a":1,"proposal_b":2,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 repairs socially unowned verification obligations in a collaborative theorem through task renewal and ledger stewardship; proposal 2 repairs illicit theorem transfer between axiom systems through an enacted premise change and instructional follow-through."},{"proposal_a":1,"proposal_b":3,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 keeps an extant proof's unresolved checking responsibilities owned; proposal 3 discharges an already-invalidated conjecture's lingering social status through archival movement, record correction, and counterexample handoff."},{"proposal_a":1,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 renews distributed obligations to verify components of a theorem; proposal 4 gives one doctoral researcher a protected choice to carry, reshape, hold, or release an open direction while separately renewing supervisory resources."},{"proposal_a":2,"proposal_b":3,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 2 is a curricular changeover that makes axiom-relative derivability salient; proposal 3 is a research-program retirement that preserves counterevidence, mathematical residue, provenance, and corrected downstream records."},{"proposal_a":2,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 2 changes students' reasoning behavior by physically and symbolically altering a displayed formal context; proposal 4 changes a power-laden advising default through student-controlled path selection and reciprocal support commitments."},{"proposal_a":3,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 3 retires the community status of a conjecture after its mathematical disposition is settled; proposal 4 revises an individual's relationship to a still-open problem without changing or retiring that problem's mathematical status."}],"replacement_indices":[],"rationale":"All four proposals are operationally complete and preserve the archetype's essential governed cycle: explicit meaning, legitimate and optional participation, marked enactment, practical consequences, memory, feedback, repair, and retirement. Their shared ritual-governance architecture is required archetype fidelity, while their affected problems, operative enactments, and causal paths remain materially different: proof stewardship, axiom-relative learning, conjecture-status retirement, and doctoral research-direction consent. All six pairs therefore constitute independent opportunities."}