{"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-residual-theory-migration-map","proposal_index":4,"version":0,"title":"Residual Impact Maps for Mathematical Theory Revisions","problem":"Changing an axiom, definition, notation-binding rule, or trusted dependency in a machine-checked mathematical theory can affect many downstream theorems. A batch checker can revalidate the corpus, but maintainers may still need to inspect a large theorem-by-theorem migration report. Static dependency reachability can over-report harmless consequences and miss effects caused by elaboration, automation, or undeclared semantic coupling. Reviewing every unchanged outcome consumes attention, while reviewing only predicted failures risks concealing an unexpected break, an unintended new dependency, or a theorem that continues to pass for the wrong reason.","actors":["mathematician proposing the foundational revision","theory-library maintainer responsible for migration approval","trusted batch checker or proof kernel","reviewers assigned to affected mathematical components","maintainer of the predictive impact model","independent auditor sampling complete theorem records"],"observable_state":"For one proposed theory revision, capture the pre-revision theorem ledger, changed foundational objects, declared and realized dependencies, predicted post-revision status of every theorem, actual batch-checker status, proof-obligation changes, trust-boundary changes, diagnostics, checker provenance, and reviewer handling time. Observable symptoms are migration reports dominated by outcomes matching predictable dependency effects, unexpected failures or survivals scattered through the report, and discrepancies between declared dependency reachability and realized checker behavior.","consequence":"Maintainers may spend scarce review attention repeatedly confirming expected migration outcomes, yet a selective impact report without synchronization, complete theorem coverage, and independent audits could hide a material consequence of the foundational change.","affected_objective":"Reduce redundant human inspection and migration-report volume while preserving complete batch revalidation, theorem-level status reconstruction, visibility of trust and dependency changes, and authoritative human approval of the revised theory.","intervention":"Before running a batch migration, freeze a versioned impact model that predicts each theorem's post-revision status, expected changed obligations, and dependency deltas from the proposed foundational edit, the pre-revision dependency structure, theorem metadata, and the model's declared scope. Run the trusted checker over the complete authorized corpus independently of those predictions. Compare every actual theorem outcome with its expected outcome and encode a typed residual: unexpected failure or survival, diagnostic change, altered obligation, dependency addition or removal, changed trusted assumption, timeout, missing result, or confidence disagreement. Reconstruct the complete migration ledger as prediction plus residual, but route reviewer attention primarily to consequence- and precision-weighted mismatches. Theorem statements, axioms, admitted facts, trust-boundary changes, removed obligations, checker failures, missing results, and any theorem outside model scope always travel in full. Verified residuals may revise the impact model or reveal missing dependency edges only through a separately reviewed update. Random predicted-unaffected theorems and risk-stratified boundary cases receive independent full-record audits; component-level snapshots resynchronize the ledger; and version mismatch, structured residual drift, coverage failure, reconstruction error, or audit disagreement decompresses the affected component to a complete theorem-by-theorem migration report.","structural_mapping":[{"archetype_element":"Prediction target and observation boundary","domain_realization":"The target is each theorem's complete post-revision migration state: checker disposition, obligations, realized dependencies, trust status, diagnostics, completion state, and assigned mathematical component."},{"archetype_element":"Generative model state","domain_realization":"A versioned theory-impact model predicts migration outcomes from the foundational edit, pre-revision dependency structure, theorem features, checker configuration, and prior validated migration residuals."},{"archetype_element":"Model scope and horizon","domain_realization":"The model is authorized for one named theory revision and one complete batch-check horizon over specified library components, checker versions, automation rules, and dependency semantics."},{"archetype_element":"Expected and actual behavior","domain_realization":"Predicted theorem outcomes are frozen before migration; actual outcomes are produced independently by the trusted checker over the complete corpus."},{"archetype_element":"Prediction comparator","domain_realization":"A structured comparator preserves unexpected pass or failure, diagnostic substitutions, obligation additions or removals, dependency changes, trust changes, timeouts, and missingness rather than reducing them to a binary alert."},{"archetype_element":"Prediction-error signal","domain_realization":"Each residual carries the theorem identity, expected and actual status difference, change provenance, impact-model version, checker version, and sufficient context to reconstruct the migration ledger."},{"archetype_element":"Precision and consequence weighting","domain_realization":"Residual priority reflects model calibration, checker completeness, theorem criticality, dependency depth, trust consequences, and review cost; protected trust and obligation changes bypass ranking."},{"archetype_element":"Residual propagation and reconstruction","domain_realization":"The review system presents selected migration residuals while reconstructing all predicted records against the matching frozen impact model and verifying their canonical digests."},{"archetype_element":"Update rule","domain_realization":"Reviewed residuals may propose missing dependency edges, revised impact classes, or changed uncertainty, but updates are versioned and cannot alter the observations or predictions of the migration already under review."},{"archetype_element":"Synchronization, freshness, and provenance","domain_realization":"Impact-model, theory, checker, automation, dependency-graph, and corpus-manifest fingerprints must match before a residual is interpreted; the authorization expires after the named migration."},{"archetype_element":"Drift and residual-error budget","domain_realization":"The system monitors residual rate and structure by component, unexplained dependency changes, audit disagreement, missing outputs, and cumulative reconstruction error under a consequence-weighted budget."},{"archetype_element":"Independent raw-state audit","domain_realization":"Uniformly random predicted-unaffected theorems and risk-stratified theorems near changed foundations are reviewed with complete pre- and post-revision records through a selection path independent of residual magnitude."},{"archetype_element":"Safety-critical bypass and fallback","domain_realization":"Changes involving statements, axioms, admitted facts, trusted dependencies, removed obligations, checker errors, missing results, or out-of-scope components always receive full records; validity failure restores the full component report."},{"archetype_element":"Attention and bandwidth budget","domain_realization":"The evaluation accounts separately for complete batch-check cost, report volume, reviewer time, model maintenance, audits, resynchronization, fallback, and missed protected consequences."}],"mechanism_mapping":[{"mechanism_slug":"predictive_codec","role":"Represent the complete theorem migration ledger through a frozen impact prediction plus typed theorem-level corrections.","counterfactual_removal":"The system would be an alert sorter rather than a reconstructible predictive representation of the migration."},{"mechanism_slug":"anomaly_detection_model","role":"Model expected migration outcomes by change class and identify theorem results that depart from their predicted component pattern.","counterfactual_removal":"Unexpected survivals, failures, or dependency changes would lack a consistent model-relative screening rule."},{"mechanism_slug":"event_triggered_residual_reporting","role":"Route model-relative theorem discrepancies to reviewers while complete checker coverage and heartbeats make the absence of a residual distinguishable from a missing result.","counterfactual_removal":"Reviewers would receive every theorem record in full, eliminating the attention-routing intervention."},{"mechanism_slug":"precision_weighted_error_gate","role":"Prioritize nonprotected residuals by reliability, mathematical consequence, trust implications, dependency position, and review cost.","counterfactual_removal":"Numerous low-consequence diagnostics could crowd out a small dependency or obligation change with larger mathematical implications."},{"mechanism_slug":"confidence_threshold_table","role":"Version the mapping from theorem class, model confidence, and residual type to suppress, display, require full context, or halt component review.","counterfactual_removal":"The migration's review policy would remain implicit and could be tuned toward a convenient queue rather than an error budget."},{"mechanism_slug":"model_version_checksum_handshake","role":"Confirm compatibility of the theory revision, corpus manifest, impact model, checker, automation configuration, and dependency semantics before reconstruction.","counterfactual_removal":"A theorem residual could be applied to a different migration baseline and silently produce a false ledger entry."},{"mechanism_slug":"periodic_full_state_resynchronization","role":"Reconcile complete component manifests and insert full theorem-state snapshots at component boundaries or early drift triggers.","counterfactual_removal":"Missing, duplicated, or misordered theorem records could corrupt the reconstructed migration ledger without a bounded repair point."},{"mechanism_slug":"shadow_raw_channel_sampling","role":"Send random predicted-unaffected and risk-stratified theorem records through an independent complete-review path.","counterfactual_removal":"The impact model could not reveal theorem classes that it systematically labels unaffected and therefore suppresses."},{"mechanism_slug":"residual_comparison_test","role":"Test residuals for component, tactic, dependency-depth, or theorem-feature structure and compare them with static dependency reachability and raw audits.","counterfactual_removal":"Systematic impact-model misspecification could be dismissed as unrelated theorem noise."},{"mechanism_slug":"model_drift_monitoring","role":"Monitor residual distributions, calibration, missing-result rates, dependency discrepancies, corpus coverage, and model validity throughout the batch migration.","counterfactual_removal":"A predictor invalidated by one component's automation or dependency behavior could continue suppressing its migration records."},{"mechanism_slug":"raw_signal_fallback_switch","role":"Restore complete theorem-by-theorem reporting for a component after any coverage, compatibility, trust, reconstruction, or audit failure.","counterfactual_removal":"The migration review could fail closed around the model precisely where its impact predictions are unreliable."},{"mechanism_slug":"prediction_error_replay_buffer","role":"Retain material migration residuals with complete pre-change context, actual checker records, and version provenance for later impact-model regression tests.","counterfactual_removal":"Unexpected migration effects would not become durable evidence for improving future impact predictions."},{"mechanism_slug":"prediction_error_review","role":"Require reviewers to classify material mismatches as dependency-model, checker-configuration, automation, theorem, or revision-boundary problems before authorizing a response.","counterfactual_removal":"Residuals could trigger ad hoc repairs without identifying which representation or mathematical boundary was wrong."},{"mechanism_slug":"surprise_to_action_bridge","role":"Assign each validated high-consequence mismatch to an owner with a defined action such as reverting the edit, repairing a theorem, expanding review scope, or correcting the dependency model.","counterfactual_removal":"Important migration discrepancies could remain visible but unowned and unresolved."}],"causal_chain":["A proposed foundational revision and the pre-revision theory state generate a frozen, versioned prediction for every theorem's migration outcome.","The trusted checker independently revalidates the complete authorized corpus and records explicit theorem outcomes and missingness.","A structured comparator removes expected status and dependency content while preserving unexpected failures, survivals, obligations, trust changes, diagnostics, and coverage gaps.","Protected events bypass suppression; other residuals are weighted by confidence, mathematical consequence, and reviewer capacity.","The complete migration ledger is reconstructed against the matching prediction, while reviewers concentrate on validated discrepancies rather than rereading expected outcomes.","Prediction-error review classifies each material mismatch and assigns an authorized response to the revision, theorem, checker configuration, or impact model.","Residuals update later impact-model versions and dependency knowledge only after review, leaving the current migration's prediction and actual record immutable.","Random and boundary-focused full-record audits test predicted-unaffected theorems, and residual comparisons reveal systematic misspecification.","Any audit, synchronization, reconstruction, trust, or coverage failure decompresses the affected component to complete theorem-by-theorem review before migration approval can proceed."],"baseline":"Run the trusted checker over the complete post-revision corpus and require reviewers to inspect the full migration record for every theorem, with static dependency reachability available only as a filter. Compare report volume, reviewer task performance, protected-change handling, and total operating cost on the identical migration.","nearest_rivals":["Static dependency-impact analysis, which predicts reachability from changed foundations but does not learn from actual migration errors or reconstruct a complete versioned ledger from residuals.","A full batch-check report grouped by success, failure, or component, which preserves complete outcomes but does not suppress predictable content against an explicit model.","Incremental recompilation or proof checking, which avoids recomputing unaffected artifacts but primarily optimizes checker work rather than governed reviewer attention and impact-model correction.","A source-code or theorem-text diff, which records explicit edits but cannot predict downstream proof obligations, automation behavior, or realized dependency changes.","A fixed release checklist for axioms, admitted facts, and failures, which protects selected events but lacks continuous model-relative comparison, raw audit sampling, and drift-triggered decompression."],"remaining_contrastive_claim":"The proposal's testable contrast is a theorem-level migration architecture in which a frozen model predicts the complete effect of a foundational revision, actual full-corpus checking produces typed residuals, those residuals govern human attention and later impact-model correction, and independent audits plus full-report fallback constrain suppression. This contrast does not imply novelty or superiority.","authority_safety":{"decision_authority":"The trusted checker determines formal acceptance of individual proof artifacts. The designated theory-library maintainers and mathematical reviewers determine whether the foundational revision and its migration are approved. The impact model may prioritize review and propose dependency corrections but cannot accept the migration, alter theorem statements, or waive checker results.","authorized_first_step":"Replay the protocol in read-only shadow mode on one archived or otherwise non-release-blocking theory revision with a complete retained batch-check report. Freeze the impact model and thresholds before evaluating an untouched set of theorem outcomes.","excluded_actions":["approving a theory revision from residual silence or a low residual count","skipping complete trusted checking of any theorem placed in the authorized corpus","suppressing theorem-statement, axiom, admitted-fact, trust-boundary, removed-obligation, checker-failure, timeout, or missing-result records","automatically editing proofs, dependencies, axioms, definitions, or theorem statements","automatically activating impact-model or threshold changes","deleting or replacing the canonical migration report during the first evaluation","extending predictions to unlisted components, checker configurations, or theory revisions","treating agreement between model and checker as mathematical review of the foundational revision"],"halt_rollback":"Halt residual presentation for the affected component after any protected-event omission, corpus-manifest discrepancy, missing checker output, reconstruction-digest failure, model or checker mismatch, structured residual drift, audit disagreement beyond the preregistered tolerance, or unowned high-consequence residual. Roll back by disabling the predictive view and restoring the unchanged complete batch-check report; no canonical theory artifact is modified by the shadow evaluation."},"negative_tests":{"strongest_counterevidence":"Consequences of foundational mathematical revisions may be too heterogeneous or semantically rich to predict safely at theorem level, and complete theorem records may be necessary for reviewers to recognize changes not represented in the residual schema. A grouped full checker report or static dependency analysis may deliver equivalent review performance with lower maintenance and audit cost.","problem_falsifier":"The problem is unsupported if complete migration reports contain little predictable repetition, reviewers can identify all material consequences from the baseline with negligible burden, foundational revisions affect too few theorems to constrain attention, or static grouping already isolates every relevant outcome without loss of context.","intervention_falsifier":"Reject residual-mode review if any protected change is suppressed; any complete theorem migration record cannot be reconstructed; a missing checker result appears as predicted success; random or boundary audits find consequential mismatches not routed by the model; residuals retain systematic component structure without fallback; reviewer decisions degrade relative to the full-report baseline; or model, audit, synchronization, and review costs are not lower at equal migration fidelity.","risks":["A shared impact model can create correlated blind spots across theory components.","Unexpected theorem survival may be treated as benign even when it reflects an unintended new dependency or weakened statement.","Declared dependency graphs may omit semantic coupling introduced by automation or elaboration.","A residual schema may preserve checker status while omitting mathematical context needed for judgment.","Thresholds may be tuned to reduce the review queue rather than respect the error budget.","Risk-stratified audits may emphasize known dependency boundaries and miss unfamiliar effects.","Reviewers may anchor on the predicted impact and rationalize actual discrepancies.","Protected-event definitions may fail to include a newly consequential trust or obligation class.","Frequent component fallback may erase the proposed attention savings.","Stored residuals may expose confidential details of unreleased foundational revisions." ]},"next_evidence_step":"Pre-register a shadow replay on one bounded theory migration with complete checker coverage and an untouched evaluation partition. Compare the residual interface with the full migration report using blinded insertions of unexpected theorem failures and survivals, dependency additions, removed obligations, admitted facts, missing results, manifest gaps, and version mismatches. Measure exact ledger reconstruction, protected-event recall, reviewer classification accuracy and time, audit disagreement, residual structure, fallback frequency, report volume, and total model-maintenance cost. The result can authorize only a further bounded shadow evaluation, not selective checking or migration approval.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Proposal 1 predicts command-to-command proof states inside a single derivation so a reviewer can focus on local proof-state changes. This proposal predicts theorem-level consequences of a foundational theory revision across an entire corpus; it does not compress tactic transitions and can operate using only theorem outcomes, dependency records, and batch-check results. Proposal 2 predicts invariant vectors for independently enumerated mathematical objects to surface conjecture counterexamples and refine a feature-partitioned atlas. This proposal instead begins with an intentional axiom or definition change and learns discrepancies between predicted and realized downstream migration effects; its objective is governed theory revision rather than conjecture exploration. Proposal 3 predicts neighboring certified solution enclosures in parameter space and uses numerical corrections to continue a branch. This proposal has no parameter trajectory, numerical enclosure, or correction solver; its residuals are discrete theorem-status, obligation, dependency, and trust changes generated by a corpus migration. Its actors, triggering event, prediction target, protected harms, update target, and downstream authority differ from all three earlier proposals, and it can be adopted as a batch theory-maintenance workflow without their proof-state transcript, conjecture atlas, or numerical continuation systems.","revision_record":{"parent_version":null,"progress_targets_addressed":["Initial complete formulation for proposal_index 4","Material independence from sealed proposals 1, 2, and 3"],"conceptual_changes":["Defined foundational theory migration as a theorem-level predictive impact and residual-review problem.","Separated full-corpus checker authority, migration approval authority, and impact-model learning."],"operational_changes":["Specified frozen per-migration predictions, typed theorem residuals, complete corpus checking, protected trust and obligation events, manifest synchronization, independent raw audits, component decompression, and read-only rollback.","Bound the first step to a non-release-blocking shadow replay retaining the full migration report."],"evidence_changes":["Specified untouched evaluation, blinded migration discrepancies, reconstruction testing, reviewer-performance comparison, audit disagreement, residual-structure analysis, fallback measurement, and complete cost accounting.","No external or prior-art evidence was consulted."],"claim_changes":["Restricted the proposal to a falsifiable architectural contrast and made no novelty, prevalence, demand, or effect-size claim."]}}