{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"catalytic_pathway_enablement__mathematics","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"bounded_graph_counterexample_wind_tunnel","proposal_index":4,"version":0,"title":"Bounded Counterexample Wind Tunnel for Finite-Graph Conjectures","problem":"A finite-graph research project receives candidate universal conjectures of the form “every graph satisfying P also satisfies Q.” Before attempting a proof, each contributor separately assembles example graphs, handles isomorphic duplicates, encodes the predicates, searches for violations, and validates any witness. This repeated setup makes systematic falsification expensive to start, so proof work can begin without a comparable record of which bounded cases were actually tested.","actors":["Graph theorists submitting candidate universal statements","Maintainers of the bounded graph generator and predicate grammar","Independent counterexample validators","Researchers deciding whether to pursue, revise, or abandon a proof attempt"],"observable_state":"The conjecture ledger contains statements entering proof development with heterogeneous or undocumented example testing. Case records show repeated graph-generation setup, inconsistent size and graph-class bounds, duplicate isomorphic cases, predicate-encoding errors, and purported counterexamples that require manual reconstruction before they can be trusted.","consequence":"Researchers may spend proof effort on statements refutable within a declared finite search envelope, while incomparable testing records and invalid witnesses make it difficult to distinguish a screened conjecture from one that received only informal examples.","affected_objective":"Produce auditable bounded-falsification dossiers for eligible finite-graph conjectures without treating failure to find a counterexample as proof.","intervention":"Create a versioned counterexample wind tunnel consisting of a validated isomorphism-reduced generator for declared classes of finite simple graphs, a restricted declarative grammar for supported graph predicates, a reusable evaluator, a witness minimizer, and an independently implemented validator. Intake requires an exact universal statement, graph-class conditions, supported predicates, a finite order bound, and resource limits. For each eligible conjecture, the facilitator streams canonical graph instances through the predicate test, stops on a verified P-and-not-Q witness, minimizes it within the operating envelope, and emits a reconstructable counterexample dossier. If no witness is found, it emits only the tested bound, generator version, coverage record, and resource status. Unsupported, label-dependent, nondeterministic, asymptotic, infinite, or computationally unbounded claims leave for ordinary mathematics. Queue depth, explored-instance rate, evaluator cost, validation failures, and generator health meter intake. Generator, grammar, or validator defects trigger withdrawal, repair, regression replay, and version replacement.","structural_mapping":[{"archetype_element":"Target transformation specification","domain_realization":"Transform an eligible universal finite-graph conjecture into either an independently verified counterexample dossier or an explicitly bounded no-witness-found dossier recording exactly what was tested."},{"archetype_element":"Activation barrier","domain_realization":"Each case otherwise reconstructs graph generation, isomorphism handling, predicate evaluation, search bounds, witness minimization, and validation before bounded falsification can proceed."},{"archetype_element":"Reusable facilitator","domain_realization":"A versioned canonical graph generator, predicate engine, search harness, minimizer, and validation interface repeatedly screen distinct conjectures without being consumed by any search result."},{"archetype_element":"Facilitator–substrate interface","domain_realization":"The intake contract requires a universal implication in the supported predicate grammar, a declared finite-simple-graph class, explicit order and resource bounds, and unambiguous semantics for P and Q."},{"archetype_element":"Selectivity rule","domain_realization":"The wind tunnel admits relabeling-invariant finite-graph predicates with validated executable meanings. It rejects unsupported invariants, implicit conventions, label-sensitive claims, unrestricted infinite statements, asymptotic claims, and cases whose evaluation cannot remain inside the declared resource envelope."},{"archetype_element":"Permitted pathway boundary","domain_realization":"A verified witness may refute the submitted universal statement as written. Absence of a witness within the finite envelope may not be reported as proof, probability of truth, or evidence outside the recorded graph class and bound."},{"archetype_element":"Turnover capacity","domain_realization":"Capacity is measured as completed, independently validated screening cycles per facilitator version and compute interval, together with encoding work, graphs examined, queue time, evaluation cost, witness-validation time, memory use, and incomplete searches."},{"archetype_element":"Cofactor or complement map","domain_realization":"The facilitator requires sufficient computation, a valid declarative encoding of the conjecture, reference implementations of supported invariants, storage for coverage logs, and an independent validator. These complements enable reuse but are accounted for separately."},{"archetype_element":"Saturation and interference monitoring","domain_realization":"Queue growth and occupied workers indicate saturation; declining exploration rate, predicate timeouts, isomorphism failures, inconsistent validators, malformed encodings, or memory growth indicate interference or facilitator degradation."},{"archetype_element":"Facilitator regeneration cycle","domain_realization":"After a generator, grammar, minimizer, or validator defect—or a deliberate semantic change—the affected version is withdrawn, repaired, replayed against a fixed regression corpus, independently reviewed, and replaced with a new immutable version."},{"archetype_element":"Byproduct and side-pathway guardrail","domain_realization":"Separate validation, explicit coverage labels, encoding review, and prohibited truth language guard against false witnesses, altered conjectures, duplicated isomorphic cases, incomplete searches presented as complete, and bounded survival presented as proof."},{"archetype_element":"Equilibrium neutrality","domain_realization":"The facilitator exposes a counterexample already present within the declared finite class; it does not change the conjecture's truth, prove surviving claims, or extend conclusions beyond the tested envelope."},{"archetype_element":"Accountable catalyst steward","domain_realization":"A named maintainer owns generator completeness within each declared scope, grammar semantics, fair queueing, capacity limits, regression tests, incident handling, withdrawal, and version succession but cannot declare a conjecture proved."}],"mechanism_mapping":[{"mechanism_slug":"interface_contract_design","role":"Fixes graph class, predicate semantics, finite bounds, input form, output guarantees, coverage language, version identifiers, and the prohibition on interpreting no-witness results as proof.","counterfactual_removal":"Without the contract, cases can silently use different graph conventions, bounds, or predicate meanings, making results incomparable and potentially answering a different conjecture."},{"mechanism_slug":"prevalidated_transformation_template","role":"Encodes the recurring search pattern P(G) and not Q(G), canonical-instance traversal, witness capture, minimization, validation, and bounded-result reporting while exposing only case-specific predicates and limits.","counterfactual_removal":"Without the reusable template, every contributor rebuilds the falsification path and its safeguards, restoring the activation burden and allowing reporting standards to drift."},{"mechanism_slug":"workflow_automation_or_macro","role":"Streams canonical graphs through the compiled predicates, records coverage, captures candidate witnesses, invokes minimization and validation, and logs every run for reconstruction.","counterfactual_removal":"Without automated repeated execution and logging, the graph corpus remains inert and manual testing cannot deliver auditable turnover across cases."},{"mechanism_slug":"fast_track_with_eligibility_rules","role":"Admits precisely specified finite universal claims whose predicates and graph classes are supported, while rerouting ambiguous, asymptotic, infinite, label-sensitive, or resource-unbounded questions.","counterfactual_removal":"Without selective admission, unsupported statements could be forced into approximate encodings and receive misleading results under throughput pressure."},{"mechanism_slug":"catalyst_cofactor_system","role":"Checks that predicate encodings, invariant implementations, computation, storage, declared bounds, and independent validation capacity are present and sufficient before a search starts.","counterfactual_removal":"Without explicit cofactor checks, missing compute or incomplete predicate implementations may be mistaken for negative evidence, and hidden per-case labor may be credited to the facilitator."},{"mechanism_slug":"inhibitor_and_poison_screen","role":"Screens for nondeterministic predicates, relabeling sensitivity, unsupported graph features, semantic ambiguity, excessive per-instance cost, stale versions, and malformed bounds before admission.","counterfactual_removal":"Without upstream screening, incompatible cases can monopolize capacity, corrupt coverage claims, or generate witnesses that depend on labels or implementation accidents."},{"mechanism_slug":"active_site_capacity_dashboard","role":"Displays queue depth, active searches, graph-exploration rate, evaluator cost, memory pressure, validation backlog, incomplete runs, and generator-version health.","counterfactual_removal":"Without joint queue and health visibility, slow searches could be treated as ordinary saturation when the actual cause is a defective predicate, generator drift, or resource poisoning."},{"mechanism_slug":"turnover_and_selectivity_assay","role":"Compares valid bounded-falsification dossiers per facilitator version against ad hoc screening while counting false witnesses, missed in-bound witnesses, invalid encodings, reroutes, incomplete runs, resource use, and maintenance.","counterfactual_removal":"Without the assay, easy conjectures, broader computation, or weak validation could be mistaken for catalytic leverage, while off-target or missed results remain invisible."},{"mechanism_slug":"catalyst_regeneration_protocol","role":"Defines withdrawal, repair, regression replay, independent cross-checking, replacement, and retirement when completeness, semantics, validation, or integrity cannot be restored.","counterfactual_removal":"Without regeneration and retirement, a visibly running but defective generator or validator could repeatedly issue false coverage or witness claims."},{"mechanism_slug":"small_safe_to_fail_probe","role":"Tests the wind tunnel on a bounded concealed collection of archived conjectures, including known in-bound witnesses, bounded survivors, and deliberately ineligible statements, without affecting live conjecture status.","counterfactual_removal":"Without a contained counterfactual probe, the project cannot test attribution, witness detection, rejection discipline, or epistemic labeling before researchers rely on the service."}],"causal_chain":["A researcher submits a universal finite-graph conjecture with explicit predicates, graph-class conditions, a finite bound, and resource limits.","The preflight screen checks semantic precision, relabeling invariance, predicate support, version compatibility, and cofactor sufficiency.","Eligibility rules admit only cases inside the validated operating envelope and route all others to ordinary mathematical analysis.","The reusable generator emits one canonical representative for each covered isomorphism class in the declared scope.","The evaluator applies P and Q to each instance and records the traversed coverage without changing the conjecture.","A candidate satisfying P and not Q is sent to the minimizer and then to a separately implemented validator.","A valid witness produces a reconstructable counterexample dossier; an invalid candidate triggers diagnosis rather than release.","A completed search without a witness produces only a bounded coverage dossier with explicit non-proof language.","The generator and search infrastructure return ready for the next eligible conjecture while capacity and integrity signals govern inflow.","A defect or semantic change withdraws the facilitator version and initiates repair, regression replay, independent review, and controlled replacement."],"baseline":"For each conjecture, its author or a collaborator manually selects examples, writes or adapts a one-off graph generator and predicate checker, chooses a search bound, inspects candidate witnesses, and describes the testing informally. Record setup and encoding labor, elapsed time, computation, covered graph class and order, duplicate handling, witness validity, incomplete runs, and the language used to characterize no-witness results.","nearest_rivals":["Direct mathematical disproof by constructing a counterexample from the conjecture's structure, which may be more explanatory and may reach examples outside any practical enumeration bound.","A general SAT, constraint, or finite-model encoding built separately for each conjecture, which may search larger structured spaces but incurs case-specific modeling and validation work.","A curated catalog of named or extremal graphs, which permits quick hand testing but does not establish systematic isomorphism-class coverage or a reusable closed search cycle.","Ordinary peer discussion or a conjecture seminar, which may expose conceptual counterexamples but lacks a specified bounded substrate stream, turnover measurement, validation protocol, and regeneration regime.","Immediate theorem-proving or proof-assistant work, which seeks a positive proof rather than first operating a selective bounded falsification pathway."],"remaining_contrastive_claim":"The untested contrastive hypothesis is that a validated canonical-instance stream and witness pipeline can be reused across eligible finite-graph conjectures to remove repeated bounded-search setup while preserving exact witness validity and explicit epistemic limits. Evaluation must include predicate-encoding labor, computation, missed in-bound witnesses, false witnesses, incomplete runs, rejected cases, and regeneration so the pathway is distinguishable from extra compute, a named-example catalog, per-case solver engineering, or weaker claims about truth.","authority_safety":{"decision_authority":"The research group's conjecture owner or steering group may authorize bounded screening and appoint the facilitator steward. Only ordinary mathematical proof and review processes may classify a surviving conjecture as proved, revise its official statement, or approve publication claims.","authorized_first_step":"Run a non-live archival probe on a fixed finite-simple-graph scope using concealed case dispositions, immutable generator and grammar versions, independent witness validation, and precommitted stop and reporting rules.","excluded_actions":["Reporting no witness found as proof, likelihood of truth, or evidence beyond the declared finite envelope","Changing P, Q, the graph class, or the bound after viewing results without recording a new case version","Approximating an unsupported predicate and presenting it as the submitted mathematical property","Disabling independent witness validation","Suppressing incomplete searches, timeouts, rejected cases, or generator defects","Increasing resource bounds beyond the probe authorization","Using the wind tunnel to determine authorship, priority, or publication status","Expanding to live mandatory screening before review of the bounded probe"],"halt_rollback":"Stop intake and withdraw the facilitator version upon a false witness, a missed regression witness within declared coverage, an isomorphism-completeness defect, inconsistent independent validation, semantic drift in a supported predicate, an undeclared incomplete run, or resource use beyond the preset envelope. Retract affected dossiers, restore conjectures to their prior status, preserve logs, and require repair plus full regression replay before restart."},"negative_tests":{"strongest_counterevidence":"The dominant work may be expressing each conjecture as a trustworthy executable predicate rather than generating graph instances. Structural counterexamples or conjecture-specific solver encodings may find witnesses with less total effort, while exhaustive canonical enumeration can saturate rapidly and bounded survival can create false confidence despite correct labels.","problem_falsifier":"The proposed problem is falsified if an audit shows that candidate conjectures already receive documented, comparable bounded testing; that proof effort is not spent on statements with accessible finite counterexamples; or that most candidate statements cannot be represented faithfully in a shared finite-graph predicate grammar.","intervention_falsifier":"The intervention is falsified for the tested scope if it misses a known witness inside declared coverage, emits any invalid witness, cannot reproduce its coverage, requires more total encoding-plus-search-plus-validation work than the fixed baseline, admits few representative cases, needs frequent facilitator rebuilds, or causes users to interpret bounded no-witness dossiers as proof despite safeguards.","risks":["A generator defect may omit an isomorphism class while reporting complete bounded coverage.","The submitted predicate may encode a subtly different conjecture.","A validator sharing code or assumptions with the evaluator may provide correlated false assurance.","Canonical enumeration may saturate in time, memory, or storage as the bound grows.","Witness minimization may alter a side condition and invalidate the example.","A no-witness dossier may psychologically anchor researchers toward believing the conjecture.","The supported grammar may bias attention toward easily executable invariants and away from mathematically important statements.","Queue priorities or compute allocation may become an unaccountable gatekeeping mechanism.","Unpublished conjectures or counterexamples may be exposed through shared logs.","Frequent grammar or invariant changes may make prior dossiers difficult to compare.","Faster screening may move the bottleneck to human interpretation, conjecture revision, or proof development."]},"next_evidence_step":"Select twelve archived finite-simple-graph conjectures: cases with independently documented counterexamples inside the probe's fixed order bound, cases documented as surviving that same bound, and deliberately ineligible cases involving unsupported or label-sensitive properties. Conceal dispositions from operators. Pre-register graph conventions, predicate meanings, generator version, coverage bound, resource ceilings, witness requirements, non-proof language, and immediate-stop criteria. Have one team use the wind tunnel and another perform the documented ad hoc baseline with the same bounds and compute allocation. A separate implementation validates every proposed witness and audits a sample of coverage records. Compare full encoding, setup, search, validation, and reporting work; correct witness recovery; false witnesses; missed regressions; rejection decisions; incomplete runs; and resource behavior. Introduce a controlled defect into a non-production generator copy after the first regression pass to test detection, withdrawal, repair, replay, and rollback. The probe supplies bounded local evidence and authorizes no live truth claims or scale-up.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Proposal 1 makes exact ideal-membership or non-membership determinations for polynomial identities through a verified Gröbner basis and normal-form certificates. This proposal performs bounded falsification of universal finite-graph conjectures through canonical instance generation and witness validation; a no-witness result remains explicitly inconclusive, and no polynomial ideal reduction is involved. Proposal 2 converts cross-subfield proof obstructions into human-readable lemma handoff packets through a rotating specialist clinic, trust, interpretation, and brokerage. This proposal uses a nonhuman instance-generation and testing facilitator, requires a formally executable conjecture, and produces empirical finite-scope dossiers rather than coordination packets. Proposal 3 transports already-proved theorems across a fixed matrix–linear-map equivalence. This proposal starts with unproved conjectures, searches their declared model class for falsifying instances, and does not derive counterpart proofs through equivalence. Its causal path—canonical instance generation, predicate evaluation, witness minimization, independent validation, bounded reporting, and generator regeneration—is independently adoptable without any earlier intervention.","revision_record":{"parent_version":null,"progress_targets_addressed":["Initial schema-complete proposal at index 4","A materially distinct conjecture-screening problem and bounded-falsification intervention","Explicit facilitator reuse, selectivity, turnover, cofactors, regeneration, authority, safeguards, falsifiers, rivals, and first evidence","Diversity explanation covering sealed proposals 1, 2, and 3"],"conceptual_changes":["Initial version; defined recurring bounded counterexample search, rather than proof, translation, or exact ideal membership, as the target transformation."],"operational_changes":["Initial version; specified a canonical graph stream, restricted predicate grammar, eligibility screen, witness minimization, independent validation, bounded-result labeling, capacity monitoring, and facilitator withdrawal."],"evidence_changes":["Initial version; defined a twelve-case concealed archival comparison with regression witnesses, ineligible cases, coverage auditing, and a controlled regeneration exercise."],"claim_changes":["Initial version; limited the proposal to an untested hypothesis about amortized bounded-falsification setup, prohibited truth inference from no-witness results, made no effect-size claim, and marked prior art unsearched."]}}