{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"representation_independent_interface_contract__mathematics","portfolio_valid":true,"proposal_assessments":[{"proposal_index":1,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally complete and faithful: it defines polynomial meaning independently of storage, hides representations, specifies laws and failures, requires abstraction functions, and gates substitution with shared black-box evidence. Its coefficient-function problem and algebraic-conformance path are distinct."},{"proposal_index":2,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally complete and faithful: it replaces construction-dependent completion proofs with a universal-property contract, hidden implementations, explicit assumptions, a common theorem oracle, and substitution via unique isometry. This is not a polynomial ADT variant."},{"proposal_index":3,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally complete and faithful: it specifies certificates by observable proof-state transitions, coverage invariants, exact evidence, verdict semantics, hidden encodings, and cross-representation conformance. Its affected object is proof evidence rather than a mathematical object construction."},{"proposal_index":4,"complete":true,"causally_faithful":true,"materially_distinct":true,"reason":"Operationally complete and faithful: it makes the labeled-graph probability measure and observation laws the binding contract, hides sampling and storage representations, and tests measure-preserving substitution. Its stochastic population-preservation path is distinct from the other three."}],"pairwise_assessments":[{"proposal_a":1,"proposal_b":2,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 removes polynomial-proof dependence on concrete storage through coefficient-function semantics and algebraic conformance; proposal 2 removes completion-theorem dependence on a chosen construction through a universal extension property and transport by unique isometry."},{"proposal_a":1,"proposal_b":3,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 abstracts an algebraic value representation for theorem reuse; proposal 3 abstracts serialized proof evidence as a verified obligation-state machine whose coverage and exact-evidence invariants determine acceptance."},{"proposal_a":1,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 1 preserves deterministic polynomial semantics across data representations; proposal 4 preserves a stochastic graph population across sampling algorithms by fixing an exact pushforward measure and randomness contract."},{"proposal_a":2,"proposal_b":3,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 2 enables theorem transport among equivalent metric completions using universal characterization; proposal 3 enables verifier substitution among certificate encodings using explicit proof-state transitions and terminal verdict rules."},{"proposal_a":2,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 2 concerns construction-independent identity of a completed metric space and theorem transport; proposal 4 concerns distributional identity of a graph sampler and preservation of experimental population semantics."},{"proposal_a":3,"proposal_b":4,"same_problem":false,"same_intervention":false,"independent_opportunity":true,"key_difference":"Proposal 3 preserves deductive certificate validity through coverage and exact-evidence checking; proposal 4 preserves stochastic sampling meaning through an exact uniform measure, independence premises, and distribution-level conformance."}],"replacement_indices":[],"rationale":"All four proposals specify an observable behavioral surface, hidden representation, invariants or laws, error and side-effect boundaries, a representation-to-semantics mapping, a shared conformance oracle, and a substitutability rule. Each also supplies bounded evidence, falsifiers, risks, authority limits, and rollback conditions. Their affected problems, interventions, and causal paths are mutually independent: algebraic-value abstraction, universal-property theorem transport, proof-certificate state verification, and stochastic measure preservation."}