{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"predictive_residual_processing__mathematics","portfolio_valid":true,"proposal_assessments":[{"proposal_index":1,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally specifies a bounded one-command proof-state predictor, structured reconstructible residuals, version synchronization, consequence weighting, reviewed updates, independent raw-state audits, protected full-state bypasses, fallback, baseline, falsifiers, authority, and rollback. Its opportunity is local auditing of sequential proof-state evolution."},{"proposal_index":2,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally specifies a frozen finite-family atlas, independently computed invariant vectors, typed residual routing, reconstruction, explicit missingness, model updates, coverage manifests, raw-result audits, protected counterexample and rigor bypasses, regional fallback, baseline, falsifiers, and authority. Its opportunity is exploratory discovery of counterexamples and regime boundaries across mathematical objects."},{"proposal_index":3,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally specifies a bounded continuation predictor, independently validated correction, reconstructible enclosure and certificate residuals, uncertainty updates, compatibility checks, full anchors, cold-start audits, protected branch and certification events, decompression, invalidation, baseline, and falsifiers. Its opportunity is certified continuation across adjacent parameter cells."},{"proposal_index":4,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally specifies a frozen change-impact model, complete independent corpus checking, typed theorem-migration residuals, ledger reconstruction, reviewed learning, manifests, independent theorem audits, protected trust and obligation records, component fallback, baseline, falsifiers, authority, and rollback. Its opportunity is governing the downstream effects of an intentional foundational theory revision."}],"pairwise_assessments":[{"proposal_a":1,"proposal_b":2,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 predicts sequential checker states inside derivations to reduce transcript-review repetition; proposal 2 predicts cross-sectional invariant vectors over a finite object family so residual structure directs conjecture exploration and revises an atlas."},{"proposal_a":1,"proposal_b":3,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 compresses human review of symbolic proof-state transitions; proposal 3 uses prediction and certified numerical correction along a parameter path, with cold-start solving when branch validity fails."},{"proposal_a":1,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 models one-command state evolution within ordinary proof construction, whereas proposal 4 models theorem-level causal impact from a named foundational edit across a corpus. The former reconstructs local proof states; the latter reconstructs a migration ledger and uses mismatches to expose dependency or elaboration effects."},{"proposal_a":2,"proposal_b":3,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 2 performs cross-sectional pattern prediction over independently enumerated objects to find counterexamples or partition boundaries; proposal 3 performs sequential local continuation of certified solution branches, where residuals update step size and trigger full recomputation near singularities."},{"proposal_a":2,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 2 predicts intrinsic invariant patterns across mathematical objects for open-ended conjecture exploration; proposal 4 predicts downstream theorem outcomes caused by an intentional theory revision for controlled migration approval."},{"proposal_a":3,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 3 reconstructs numerical enclosures and certificates along parameter-space continuation, with branch-validity safeguards; proposal 4 reconstructs discrete theorem statuses, obligations, dependencies, and trust changes after a foundational edit, with corpus-review safeguards."}],"replacement_indices":[],"rationale":"All four proposals instantiate the full predictive-residual causal loop: explicit bounded prediction, independent observation, structured and consequence-weighted residual propagation, reconstruction against synchronized model state, validated learning, drift and error monitoring, independent raw-state audits, protected bypasses, and full-state fallback. Each is operationally testable and falsifiable. Although proposals 1 and 4 both involve machine-checked mathematics, they address independently adoptable problems through different instantiated predictors and causal paths: sequential proof-state reconstruction versus change-impact inference across a theory corpus. The other pairs likewise differ in affected problem, intervention, and causal path, so no replacement is required."}