{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"representation_independent_interface_contract__mathematics","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"inequality_certificate_semantic_contract_v0","proposal_index":3,"version":0,"title":"Semantic Contract for Representation-Independent Inequality Certificates","problem":"A computer-assisted proof of an inequality over a bounded real domain emits a branch-and-bound certificate in a generator-specific tree format. Its audit script depends on node numbering, traversal order, decimal formatting, heuristic labels, and the generator's serialization layout. A different generator, a streamed certificate, or a compressed derivation DAG therefore cannot replace the original artifact even when it supplies the same exact rational bounds and domain-covering argument.","actors":["Mathematicians authoring the computer-assisted proof","Implementers of certificate generators","Maintainers of the small verification kernel","Reviewers auditing the mathematical argument","Custodians preserving the proof artifact"],"observable_state":"The verifier parses generator-specific fields, assumes a particular parent-before-child order, reconstructs omitted domain information from node identifiers, or treats floating-point text and heuristic labels as proof-relevant. Reordering independent branches or encoding shared evidence as a DAG causes rejection before any mathematical obligation changes. There is no shared state invariant stating when splitting, bounding, and closing steps constitute a complete proof of the inequality.","consequence":"The theorem's checkable evidence remains coupled to one certificate representation and generator execution trace. A representation change can invalidate the audit for non-mathematical reasons, while two superficially similar verifiers can disagree about missing coverage, malformed bounds, or incomplete branches.","affected_objective":"Preserve independently checkable validity of the fixed inequality argument while allowing certificate storage, generation strategy, and traversal representation to change.","intervention":"Define an opaque inequality-certificate component by a deterministic proof-state contract. For a fixed claim that F(x) is nonnegative on an initial rational box D, the abstract state contains the claim, declared trusted lemmas, a frontier of unresolved rational boxes, and certified closed boxes. Public steps initialize the claim, split a frontier box at a rational cut, attach an exact bound witness, close a box whose witness proves nonnegativity, and request a final verdict. Splitting must replace a parent with children whose union covers it; closing must cite evidence checked by a small exact-arithmetic kernel; no unresolved region may disappear; and Verified is returned only when the frontier is empty and the closed regions cover D. Malformed evidence returns Rejected, while an exhausted declared resource budget returns Indeterminate and cannot be promoted to Verified. Tree, DAG, and streamed representations each supply an abstraction map into these state transitions. Node identifiers, traversal order, compression, generator heuristics, caches, floating-point diagnostics, and parallel schedules are non-contractual. A shared black-box and property-based suite gates every implementation and adapter.","structural_mapping":[{"archetype_element":"Abstract component","domain_realization":"An inequality certificate understood as a finite, valid transition sequence from the initial domain obligation to an empty proof frontier."},{"archetype_element":"Observable operation surface","domain_realization":"Claim initialization, rational-box splitting, exact bound submission, obligation closure, status inspection, and final verification."},{"archetype_element":"Abstract state model","domain_realization":"The fixed claim, trusted-lemma manifest, unresolved frontier, certified closed regions, resource status, and terminal verdict."},{"archetype_element":"Behavioral laws and invariants","domain_realization":"Children cover every split parent, only checked evidence closes a region, closed and unresolved regions continue to cover the initial domain, and verification requires an empty frontier."},{"archetype_element":"Hidden representation","domain_realization":"Tree or DAG layout, event ordering, node identifiers, evidence sharing, compression, search heuristics, caches, and parallel execution traces."},{"archetype_element":"Representation invariant and abstraction function","domain_realization":"Each concrete artifact must be well-formed and map unambiguously to abstract proof-state transitions that preserve coverage and evidence validity."},{"archetype_element":"Error semantics","domain_realization":"Invalid syntax or evidence is Rejected; a valid but unfinished certificate is Incomplete; resource exhaustion is Indeterminate; none is interchangeable with Verified."},{"archetype_element":"Side-effect boundary","domain_realization":"Verification is deterministic for the certificate, contract version, trusted-lemma manifest, and resource profile; it performs no network lookup or generator callback."},{"archetype_element":"Conformance oracle","domain_realization":"One suite of valid, incomplete, malformed, coverage-breaking, and evidence-corrupting certificates is applied through only the public operations."},{"archetype_element":"Substitutability rule","domain_realization":"A representation or checker implementation is eligible for the bounded audit only if it preserves abstract verdicts, failure categories, proof-state laws, and the declared trust boundary across the shared suite."}],"mechanism_mapping":[{"mechanism_slug":"abstract_data_type_specification","role":"Defines the certificate as an abstract obligation-state machine, then requires each tree, DAG, or stream representation to provide a validity predicate and an abstraction map into that state machine.","counterfactual_removal":"Without the state model, certificate formats would expose steps without specifying what mathematical obligation each step creates, preserves, or discharges."},{"mechanism_slug":"design_by_contract_clause","role":"Gives split, bound, close, and finalize operations explicit preconditions, postconditions, and distinct failure outcomes.","counterfactual_removal":"Without per-step clauses, a checker could silently drop a region, accept an inapplicable bound, or conflate resource exhaustion with mathematical rejection."},{"mechanism_slug":"opaque_type_or_module_boundary","role":"Prevents auditors and clients from inspecting node layout or generator metadata and routes verification through the declared certificate operations.","counterfactual_removal":"Without opacity, node numbering, traversal order, and compressed storage could remain load-bearing parts of the audit."},{"mechanism_slug":"black_box_contract_test_suite","role":"Runs the same verdict and transition checks against every certificate adapter and checker implementation without reading their internal data structures.","counterfactual_removal":"Without a shared suite, each implementation could validate its own preferred fixtures while disagreeing on malformed or incomplete certificates."},{"mechanism_slug":"property_based_conformance_test","role":"Generates bounded split-and-close sequences and targeted corruptions, checking coverage, frontier preservation, terminal-state rules, and rejection of invalid evidence.","counterfactual_removal":"Without generated operation sequences, interactions among nested splits, shared evidence, and incomplete branches would be represented only by hand-selected examples."},{"mechanism_slug":"metamorphic_behavior_test","role":"Checks that renaming node identifiers, reordering independent branches, or replacing duplicated evidence with contract-equivalent shared evidence preserves the abstract verdict.","counterfactual_removal":"Without these relations, an implementation could pass fixed fixtures while still treating incidental serialization choices as mathematical content."},{"mechanism_slug":"reference_implementation_differential_test","role":"Uses a deliberately small, direct verifier over explicit rational boxes as an independent oracle for the bounded fixture corpus and compares verdicts at the contract level.","counterfactual_removal":"Without the simple reference, multiple optimized checkers or adapters could agree because they share the same normalization or coverage defect."},{"mechanism_slug":"representation_leakage_probe","role":"Subtracts promised behavior from all observable outputs and flags dependence on traversal order, error wording, timing, debug metadata, floating-point diagnostics, or decoded node identifiers.","counterfactual_removal":"Without the leakage audit, generator-specific details could become unofficial certificate requirements despite an opaque public type."},{"mechanism_slug":"semantic_versioning_and_deprecation_gate","role":"Records changes to proof steps, trusted-lemma identifiers, verdict semantics, and resource profiles so preserved certificates identify the exact contract under which they are checked.","counterfactual_removal":"Without governed versions, a checker update could reinterpret an archived certificate while continuing to report the same undifferentiated success status."},{"mechanism_slug":"abstraction_barrier_code_review","role":"Requires reviewers to classify every verifier dependency as part of the mathematical contract, a declared diagnostic, or prohibited generator reach-through.","counterfactual_removal":"Without review, expedient parsing or debugging dependencies could bypass the mechanical boundary and harden into required behavior."}],"causal_chain":["The current audit consumes a solver-specific branch-and-bound trace containing both mathematical evidence and incidental generator behavior.","Auditing code consequently relies on node order, identifiers, formatting, and reconstruction conventions not required by the inequality argument.","The intervention separates those details from an abstract frontier-and-coverage proof state with exact step obligations.","Adapters map different concrete representations into the same public transitions, and the exact kernel checks evidence without trusting the generator.","Black-box, generated, differential, and metamorphic checks reject lost coverage or invalid bounds while tolerating non-contractual reordering and compression.","Version and leakage controls keep verdict meanings, trusted lemmas, and sanctioned diagnostics explicit over time.","A conforming certificate representation or generator can therefore replace another in the bounded audit without changing the theorem claim or the verifier's mathematical acceptance rule."],"baseline":"Preserve the original generator, certificate file, parser, and execution environment together, and treat successful replay of that frozen stack as the audit criterion.","nearest_rivals":["Archive a container containing the original generator and verifier without separating proof evidence from execution details.","Choose one canonical certificate serialization and require every future generator to emit it exactly.","Write pairwise converters from each new certificate format into the incumbent tree format.","Publish raw solver logs plus a prose description and ask reviewers to inspect representative branches.","Rerun the numerical search independently instead of checking a finite proof certificate."],"remaining_contrastive_claim":"Compared with freezing the original stack, imposing one serialization, or maintaining pairwise converters, the testable claim is that the frontier, coverage, exact-evidence, and verdict contract is sufficient for a tree certificate and an independently encoded event stream to receive identical contract-level verdicts on the frozen fixture corpus even when node names, independent-branch order, compression, and generator diagnostics differ.","authority_safety":{"decision_authority":"The theorem authors and verification-kernel maintainers control the experimental contract and fixtures. Reviewers or the relevant publication authority retain sole authority to decide whether the resulting evidence is adequate for accepting the mathematical proof.","authorized_first_step":"Build an offline pilot around one non-publication-gating inequality claim with a fixed rational domain, fixed trusted-lemma manifest, bounded certificate size, and two independently written certificate adapters.","excluded_actions":["Changing the inequality claim or its domain to make a certificate pass","Treating the certificate generator as trusted proof evidence","Accepting floating-point diagnostics without an exact checked witness","Converting Rejected, Incomplete, or Indeterminate into Verified","Fetching lemmas, code, or evidence over the network during verification","Replacing mathematical or editorial review with suite conformance","Changing an archived certificate or its declared contract version","Weakening coverage or exactness laws after observing a failure"],"halt_rollback":"Stop if either adapter maps one concrete artifact ambiguously, any mutated certificate reaches Verified after losing coverage or corrupting evidence, the two checkers disagree on a frozen fixture, or the pilot requires expanding the trusted kernel without review. Roll back by removing the isolated adapters and contract runner; retain the original artifact and verifier unchanged."},"negative_tests":{"strongest_counterevidence":"The existing audit may already pass all generator output through a small deterministic exact checker whose inputs have representation-independent coverage and evidence semantics. If a tree, stream, and DAG can be adapted without changing checker behavior or audit code, the proposed new contract would mainly restate an existing boundary.","problem_falsifier":"A dependency inventory finds that node order, identifiers, formatting, heuristics, and floating diagnostics are confined to untrusted parsing, while all acceptance decisions already depend solely on exact bounds, complete domain coverage, and an explicit terminal rule.","intervention_falsifier":"Two artifacts map to the same abstract transition sequence and declared trust manifest but receive different contract-level verdicts, or the shared contract admits a certificate that omits part of the initial domain or closes a region without valid exact evidence.","risks":["The abstract transition model may normalize away an ordering dependency that is mathematically relevant to scoped assumptions or evidence availability.","The trusted arithmetic kernel or lemma manifest may contain an error that every certificate representation inherits.","Generated fixtures may fail to exercise a malformed sharing pattern, boundary overlap, or degenerate rational box.","Exact arithmetic and fully explicit coverage evidence may exceed the pilot's declared resource profile, producing inconclusive checks.","An overly prescriptive step algebra could freeze one proof strategy even while allowing multiple storage formats.","A simple reference verifier may share parsing or arithmetic code with the candidate and agree on the same defect.","Contract version changes may fragment preserved certificates or encourage unsupported legacy paths.","Stable error categories or diagnostics may accidentally become stronger promises than mathematical auditing requires."]},"next_evidence_step":"Freeze one bounded inequality claim, its rational domain, trusted-lemma manifest, resource profile, and 24 fixtures before implementing the contract. The fixtures must include valid proofs, unfinished frontiers, omitted children, overlapping and degenerate splits, corrupted rational bounds, unknown lemma identifiers, reordered independent branches, and renamed nodes. Implement a direct explicit-tree verifier, an independently parsed event-stream adapter, and the abstract state checker without shared parsing code. Compare their verdicts, run the metamorphic transformations, and confirm that each seeded coverage or evidence defect is rejected. Record every disagreement, unmodeled observable, trust-boundary expansion, and resource exhaustion; do not alter or replace any publication evidence.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Proposal 1 addressed theorem proofs coupled to a finite polynomial's ordered-list storage; it introduced coefficient-function semantics and an opaque algebraic operation surface. Proposal 2 addressed results coupled to a particular construction of metric completion; it introduced a universal extension property and substitution through unique isometry. This proposal instead addresses the audit evidence for a computer-assisted inequality proof. Its intervention is a deterministic certificate state machine with coverage, exact-evidence, verdict, trust, and version contracts. Its causal path runs from solver-trace dependence through semantic proof-state reconstruction to representation-independent verification, rather than from data representation to algebraic conformance or from constructed objects to universal-property transport. It is independently adoptable within one certificate-audit pipeline and requires no polynomial abstraction or metric-completion package.","revision_record":{"parent_version":null,"progress_targets_addressed":["Third complete proposal","Materially different proof-audit problem","Distinct state-transition intervention and causal path","Explicit diversity from proposals 1 and 2","Bounded reversible first evidence"],"conceptual_changes":["Initial version defines a branch-and-bound certificate by obligation-state transitions, coverage invariants, exact evidence, and terminal verdict semantics."],"operational_changes":["Initial version confines the pilot to one frozen inequality claim, two independent representations, a small checker, and 24 predetermined fixtures."],"evidence_changes":["Initial version specifies differential verdict checks, seeded corruptions, metamorphic representation changes, trust-boundary review, and resource-status recording."],"claim_changes":["The claim is limited to representation-independent verification of the bounded fixture corpus and makes no assertion of novelty, prevalence, demand, or effect size."]}}