{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"predictive_residual_processing__mathematics","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"prp-math-proof-state-residual-review","proposal_index":1,"version":0,"title":"Residual Proof-State Transcripts for Auditing Large Formal Derivations","problem":"In a large machine-checked derivation, each proof command can generate a complete proof state containing goals, hypotheses, inferred types, dependencies, and diagnostics. Authors and reviewers may repeatedly inspect or exchange these mostly predictable states, consuming storage and review attention while the few consequential changes—such as a new axiom dependency, an altered goal, an unresolved obligation, or an unexpected elaboration choice—remain difficult to isolate. Merely showing exceptions would be unsafe because an incorrect or stale expectation could suppress the evidence needed to audit the proof.","actors":["formal proof author","independent proof reviewer","proof-assistant kernel or trusted checker","maintainer of the proof-state prediction and reconstruction pipeline","repository or review-system administrator"],"observable_state":"For a bounded corpus of formal derivations, record each command, its full pre-command and post-command proof states, provenance, checker version, elapsed review time, and state size. Observable symptoms are a high repeated-content fraction between predicted and actual post-command states, long full-state transcripts, reviewer navigation dominated by unchanged context, and consequential state changes interspersed with routine transformations.","consequence":"Reviewers spend scarce attention reconstructing routine proof evolution, yet a residual-only shortcut without synchronization and raw access could conceal a material change or make a proof state appear valid against the wrong predictor.","affected_objective":"Reduce transcript volume and routine review effort while preserving exact reconstruction, kernel-level proof acceptance, dependency visibility, and reviewer access to complete proof states.","intervention":"Create a replayable proof-review transcript in which a versioned predictor derives the expected post-command proof state from the prior full state, command, environment, and declared scope. Compare that expectation with the checker-produced state; encode the structured residual over goals, hypotheses, types, dependencies, warnings, and obligations; and present reviewers primarily with precision- and consequence-weighted residuals plus reconstructible context. Tag every residual with predictor, library, environment, and checker versions. Preserve full theorem statements, axioms, trust-boundary changes, final kernel certificates, errors, and designated dependency events through an unconditional full-state bypass. Independently retain random and risk-stratified full-state samples, periodically re-anchor the transcript with complete states, and switch the affected proof segment to full-state review after version mismatch, missing output, reconstruction failure, structured residual drift, or an out-of-scope command. Residuals may improve later predictions only through a separately reviewed, versioned update; they never determine theorem acceptance.","structural_mapping":[{"archetype_element":"Prediction target and observation boundary","domain_realization":"The target is the complete checker-produced post-command proof state for one command, including ordered goals, local hypotheses, inferred types, dependency changes, obligations, warnings, and provenance."},{"archetype_element":"Generative model with bounded scope and horizon","domain_realization":"A versioned predictor forecasts exactly one post-command state from the preceding anchored state, the submitted command, and a fixed proof environment; unsupported commands or environments are outside scope."},{"archetype_element":"Expected and actual behavior","domain_realization":"The expected state is generated before comparison; the actual state comes independently from the trusted checker and remains available for audit."},{"archetype_element":"Signed or structured prediction comparator","domain_realization":"A canonical tree comparison records additions, removals, substitutions, reorderings, and dependency changes rather than collapsing mismatch into one score."},{"archetype_element":"Precision and consequence weighting","domain_realization":"Residual priority reflects predictor calibration and source completeness, while axiom, trust-boundary, theorem-statement, obligation, and kernel-error changes receive mandatory full treatment regardless of size."},{"archetype_element":"Residual propagation and reconstruction","domain_realization":"The review interface carries the structured delta with baseline identity; the full state is reconstructed by applying it to the matched predicted state and checked against a canonical digest."},{"archetype_element":"Update rule","domain_realization":"Validated residuals enter a replay set for proposed predictor revisions, but a new predictor version is activated only after held-out reconstruction tests and maintainer approval."},{"archetype_element":"Synchronization, freshness, and provenance","domain_realization":"Residual interpretation is gated on matching predictor, checker, library, and environment fingerprints, with complete-state anchors bounding accumulated divergence."},{"archetype_element":"Independent raw audit","domain_realization":"Random proof steps and risk-stratified steps are retained and reviewed in complete form through a path that does not use the predictor's reconstruction."},{"archetype_element":"Fallback and decompression","domain_realization":"Any checksum mismatch, missing heartbeat, unsupported command, failed digest, excessive cumulative residual, drift signal, or protected event causes full-state display and retention for the affected segment."},{"archetype_element":"Attention and error budgets","domain_realization":"The pilot accounts separately for transcript bytes, predictor and audit costs, reviewer time, exact reconstruction failures, and missed protected changes; savings do not excuse any protected-event omission."}],"mechanism_mapping":[{"mechanism_slug":"predictive_codec","role":"Generate matched expected proof states and encode each actual checker state as a structured, reconstructible residual.","counterfactual_removal":"Without it, the system is only an anomaly display or ordinary diff and lacks model-relative reconstruction."},{"mechanism_slug":"model_version_checksum_handshake","role":"Gate every residual on compatible predictor, checker, library, and environment fingerprints.","counterfactual_removal":"A well-formed residual could be applied to the wrong mathematical environment and silently reconstruct a false state."},{"mechanism_slug":"precision_weighted_error_gate","role":"Allocate reviewer attention among residuals using calibration, source quality, consequence class, and a declared review budget.","counterfactual_removal":"Large cosmetic changes could crowd out small but consequential dependency or obligation changes."},{"mechanism_slug":"confidence_threshold_table","role":"Version the rules mapping residual class and predictor confidence to suppress, display, require full context, or halt.","counterfactual_removal":"The review policy would be implicit and thresholds could change without an attributable error-budget decision."},{"mechanism_slug":"periodic_full_state_resynchronization","role":"Insert complete proof-state anchors on a fixed cadence and after evidence of divergence.","counterfactual_removal":"One lost or misapplied residual could corrupt all later reconstructions without a bounded recovery point."},{"mechanism_slug":"shadow_raw_channel_sampling","role":"Retain random and risk-stratified complete states for independent comparison with reconstructed states.","counterfactual_removal":"The pipeline could not observe content that its own predictor and gate systematically suppress."},{"mechanism_slug":"residual_comparison_test","role":"Test residuals for persistent structure by command class and compare them with a simpler predictor and raw samples.","counterfactual_removal":"Systematic misspecification could be mislabeled as harmless residual noise."},{"mechanism_slug":"model_drift_monitoring","role":"Monitor reconstruction disagreement, residual distribution, unsupported-command rate, and predictor staleness across environment changes.","counterfactual_removal":"A predictor could retain suppression authority after the proof language or library has moved outside its validated scope."},{"mechanism_slug":"raw_signal_fallback_switch","role":"Replace residual presentation with complete proof states whenever validity or protected-event conditions fail.","counterfactual_removal":"The system would fail closed around an uncertain model and could conceal precisely the states it cannot predict."},{"mechanism_slug":"prediction_error_replay_buffer","role":"Store selected residuals with complete context and version provenance for diagnosis and bounded predictor revision.","counterfactual_removal":"Errors would be transient alerts rather than attributable evidence for regression testing and learning."}],"causal_chain":["A one-step, versioned predictor represents the routine evolution of a proof state from the preceding state and command.","The trusted checker independently produces the actual post-command state.","A canonical structured comparison separates predicted content from additions, removals, substitutions, and dependency changes.","Precision and consequence rules route protected changes in full and concentrate review attention on other informative residuals.","A reviewer reconstructs surrounding context from the matched prediction plus residual, while a digest tests exact reconstruction.","Validated residuals populate a provenance-preserving replay set, supporting slower and separately authorized predictor updates.","Version handshakes, full-state anchors, drift monitoring, and independent raw samples expose desynchronization and systematic suppression.","Validity failure immediately decompresses the affected segment to complete proof states, preserving auditable review and leaving theorem acceptance solely to the trusted checker."],"baseline":"Store and display every complete checker-produced proof state in command order, with ordinary text search and manual reviewer navigation; measure transcript volume, protected-event detection, reconstruction fidelity, reviewer time, and total processing cost without predictive suppression.","nearest_rivals":["A syntax or abstract-syntax-tree diff between successive proof scripts, which shows edited source but does not predict or reconstruct checker states.","A proof-dependency graph or axiom linter, which highlights selected trust and dependency properties but does not encode the rest of each proof state as a model-relative residual.","A fixed exception dashboard that displays checker errors and warnings but lacks a versioned generative baseline, residual learning loop, raw audit sample, and decompression path.","A complete proof-state log with folding or summarization, which preserves all states but does not make prediction error the transmitted and updating representation."],"remaining_contrastive_claim":"The proposal's testable contrast is the coupled architecture: a shared one-step model predicts complete proof states; structured residuals become the primary review message; exact reconstruction is checked against versioned baselines; and independent raw samples plus automatic full-state fallback govern what prediction may suppress. No claim is made that this architecture is novel or superior before testing.","authority_safety":{"decision_authority":"The trusted proof-assistant kernel alone determines formal acceptance. Human reviewers retain authority over mathematical interpretation and approval. A designated maintainer may propose predictor or threshold revisions, but activation requires repository-owner approval after the bounded evidence test.","authorized_first_step":"Run an offline, read-only replay on an archived, non-release-blocking proof corpus. Generate residual views and reconstructions beside the existing complete transcripts without changing proof acceptance, reviewer assignments, repository contents, or retention policy.","excluded_actions":["accepting, rejecting, or modifying a theorem from a residual score","suppressing theorem statements, axioms, trust-boundary changes, unresolved obligations, checker errors, or final kernel certificates","deleting or replacing canonical proof scripts or checker outputs","training on or exposing material outside the approved archived corpus","activating predictor or threshold updates automatically","using silence as evidence of a valid proof state without a checker output, heartbeat, matching version, and reconstruction check"],"halt_rollback":"Halt residual presentation for the affected scope after any protected-event omission, digest mismatch, version mismatch, missing checker output, audit disagreement beyond the preregistered tolerance, or unexplained structured drift. Roll back by disabling the predictive view and returning to the unchanged full-state transcript; because the pilot is side-by-side and read-only, canonical proof artifacts require no restoration."},"negative_tests":{"strongest_counterevidence":"Complete proof states may contain decision-relevant context that cannot be safely ranked as predictable, or the predictor, synchronization, audit, and reconstruction work may cost at least as much reviewer attention and storage as the full transcript. Either result would remove the intervention's rationale.","problem_falsifier":"On the bounded corpus, the problem is not supported if successive proof states lack substantial reconstructible regularity, if reviewers do not spend measurable time traversing repeated state content, or if consequential changes are already isolated reliably by the baseline at negligible marginal cost.","intervention_falsifier":"Reject residual-mode authorization if any protected change is omitted; any sampled full state cannot be reconstructed exactly at its canonical representation; version or missing-output failures are presented as confirmation; residuals retain systematic structure that the fallback rules fail to catch; or total prediction, metadata, audit, fallback, and review cost is not lower than the complete-transcript baseline at equal audit fidelity.","risks":["A shared predictor and reviewer interface could create correlated blind spots.","Canonicalization might erase order, naming, or provenance distinctions that matter to interpretation.","Thresholds could be tuned for a quiet review queue instead of the declared error budget.","Rare command forms may be absent from the audit sample.","Residuals may expose unusual proof structure more clearly than complete states, creating confidentiality concerns.","Frequent fallback or full-state anchoring may eliminate any capacity advantage.","Reviewers may over-trust a compact residual view even though kernel acceptance and mathematical understanding remain separate judgments."]},"next_evidence_step":"Pre-register a replay on one fixed archived corpus and an untouched holdout. Compare the proposed view with complete-state review using exact canonical reconstruction checks, blinded insertion of protected dependency and obligation changes, random plus risk-stratified raw-state audits, reviewer task time, false suppression counts, fallback frequency, transcript bytes, and total computation and maintenance effort. The result licenses at most a second read-only evaluation; it does not authorize deployment or proof acceptance changes.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Not assessed against prior proposals; this is proposal_index 1, and no prior candidate is used as evidence or design input.","revision_record":{"parent_version":null,"progress_targets_addressed":["Initial complete proposal"],"conceptual_changes":["Initial formulation of proof-state review as a reconstructible residual channel rather than a generic anomaly alert."],"operational_changes":["Defined a read-only archived-corpus pilot, protected event classes, exact reconstruction checks, independent raw audits, synchronization gates, and full-state rollback."],"evidence_changes":["Specified bounded baseline comparison, holdout replay, blinded protected-change tests, and cost accounting; no external evidence was consulted."],"claim_changes":["Limited the claim to a testable architectural contrast and made no novelty, prevalence, demand, or effect-size claim."]}}