{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"catalytic_pathway_enablement__mathematics","portfolio_valid":true,"proposal_assessments":[{"proposal_index":1,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally complete: it specifies an eligible recurring ideal-membership transformation, fixed interface, reusable verified Gröbner basis, certificate checking, selectivity, turnover, saturation and interference monitoring, regeneration, deactivation, authority, counterfactual, falsifiers, and a bounded probe. The basis is released unchanged after each reduction and restored or replaced after context drift, preserving the catalytic cycle."},{"proposal_index":2,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally complete and faithful: a rotating clinic repeatedly lowers cross-subfield translation, trust, search, and handoff barriers, releases each lemma packet, and regenerates through documentation, rotation, rest, conflict controls, and artifact refresh. Eligibility, capacity, fidelity review, escalation, stewardship, falsifiers, and bounded evaluation are explicit. Its human coordination problem and intervention are distinct from the computational proposals."},{"proposal_index":3,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally complete and faithful: an established equivalence bundle repeatedly transports already-proved theorems between representations, remains available after each turnover, and is withdrawn and revalidated after definition or API drift. The proposal defines the interface, supported grammar, cofactors, kernel and human checks, capacity, selectivity, deactivation, counterfactual, falsifiers, and probe. It is not merely a renamed reduction lane because it preserves proofs across representations rather than deciding ideal membership."},{"proposal_index":4,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally complete and faithful: a reusable canonical graph stream and witness pipeline lowers repeated bounded-falsification setup, returns ready after each conjecture, meters capacity, rejects incompatible claims, independently validates witnesses, labels bounded survival as inconclusive, and regenerates defective versions. Authority, safeguards, counterfactual, falsifiers, and an archival probe are explicit. Its affected problem and search-to-witness causal path are unique in the portfolio."}],"pairwise_assessments":[{"proposal_a":1,"proposal_b":2,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 resolves exact polynomial ideal-membership cases with a verified Gröbner reducer and certificates; proposal 2 prepares cross-subfield lemma handoffs through rotating human translation and brokerage. They affect different bottlenecks and neither intervention is required by the other."},{"proposal_a":1,"proposal_b":3,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 classifies candidate polynomial identities by normal-form reduction against a fixed ideal; proposal 3 transports an already-proved theorem across a matrix–linear-map equivalence. Their reusable formal artifacts are analogous at the archetype level, but their transformations, interventions, outputs, and causal paths are materially different."},{"proposal_a":1,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 makes exact ideal-membership determinations using algebraic reduction and proof certificates; proposal 4 screens unproved finite-graph conjectures by canonical enumeration and verified counterexample search, with bounded non-findings explicitly inconclusive."},{"proposal_a":2,"proposal_b":3,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 2 addresses informal cross-field interpretation, trust, and ownership through a governed human clinic producing lemma packets; proposal 3 addresses repetitive formal representation transport through a verified equivalence bundle producing kernel-checked counterpart theorems."},{"proposal_a":2,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 2 catalyzes coordination before substantive proof work through specialists and brokerage; proposal 4 catalyzes bounded empirical falsification through graph generation, executable predicates, minimization, and independent witness validation."},{"proposal_a":3,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 3 starts from proved theorems and derives faithful counterparts through equivalence and kernel checking; proposal 4 starts from unproved universal conjectures and searches a bounded model class for falsifying instances. Proof transport and counterexample search have distinct outputs and causal mechanisms."}],"replacement_indices":[],"rationale":"Every proposal supplies a feasible recurring transformation, a specific reusable facilitator, an explicit substrate interface and selectivity boundary, measurable multi-cycle turnover, capacity and degradation monitoring, regeneration or retirement, equilibrium neutrality, accountable authority, counterfactual comparison, falsifiers, and a bounded evidence step. All six pairs differ simultaneously in the affected problem, intervention, and causal path. Shared governance and measurement mechanisms instantiate the common archetype but do not collapse the proposals into variants of one opportunity."}