{"schema_version":1,"research_id":"eoa_inverse_innovation_exp06_external_evaluation_20260803","source_assessment_id":"catalytic_pathway_enablement__mathematics:P4:v0","cell_id":"catalytic_pathway_enablement__mathematics","search_queries":["finite graph conjecture counterexample exhaustive generation nauty geng official documentation","House of Graphs database counterexample conjecture official paper","automated conjecturing graph theory counterexample generation research paper","SageMath nauty geng graphs documentation","site:pallini.di.uniroma1.it nauty geng user guide pdf","graph theory exhaustive generation test conjectures counterexamples nauty paper","GraPHedron graph invariant conjectures counterexamples paper","graph theory software conjecture testing counterexample generator database paper","site:pallini.di.uniroma1.it nauty user guide geng 2.8.8","Brendan McKay nauty Traces user guide PDF geng official","nauty geng official webpage generate non-isomorphic graphs","\"A computational attack on the conjectures of Graffiti\" pdf","\"tested approximately 200\" Graffiti conjectures counterexamples 40 PDF"],"sources":[{"source_id":"S1","title":"The nauty Traces page","publisher":"Brendan McKay, Australian National University","url":"https://users.cecs.anu.edu.au/~bdm/nauty/","source_class":"OFFICIAL_PRODUCT_DOCUMENTATION","publication_date":"n.d.","accessed_at":"2026-08-03","claims_supported":["nauty and Traces compute graph automorphisms and canonical labels.","The bundled geng utility rapidly generates non-isomorphic graphs, with generators also available for several restricted graph classes.","Versioned, reusable canonical-generation infrastructure already exists."]},{"source_id":"S2","title":"Common graphs — SageMath Graph Theory Reference Manual","publisher":"SageMath","url":"https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_generators.html","source_class":"OFFICIAL_PRODUCT_DOCUMENTATION","publication_date":"2026","accessed_at":"2026-08-03","claims_supported":["SageMath exposes a generator that iterates over distinct, exhaustive isomorphism-class representatives.","SageMath provides an interface to nauty geng.","Documentation warns that property-directed generation can omit graphs unless the property satisfies required inheritance conditions, illustrating a concrete completeness hazard."]},{"source_id":"S3","title":"House of Graphs 2.0: a database of interesting graphs and more","publisher":"arXiv; authors affiliated with Ghent University","url":"https://arxiv.org/abs/2210.17253","source_class":"PRIMARY_RESEARCH","publication_date":"2022-10-31","accessed_at":"2026-08-03","claims_supported":["House of Graphs hosts complete lists of pairwise non-isomorphic graphs for multiple classes and a searchable database containing counterexamples.","Its stated purpose includes giving users a good chance of finding counterexamples or judging a graph-theoretic situation.","Users extend the database, and maintainers rebuilt the system for maintainability and expansion."]},{"source_id":"S4","title":"DIMACS Working Group on Computer-Generated Conjectures from Graph Theoretic and Chemical Databases I","publisher":"DIMACS, Rutgers University","url":"https://dimacs.rutgers.edu/archive/SpecialYears/2001_Data/Conjectures/conjecturesdescription.html","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"2001","accessed_at":"2026-08-03","claims_supported":["The working group documented multiple graph-conjecturing and testing systems.","VEGA was described as allowing researchers, teachers, and students to test ideas quickly on small and mid-size examples.","The group explicitly sought to give a larger research community opportunities to use such systems."]},{"source_id":"S5","title":"Graffiti (from Written on the Wall): A Computational Attack on the Conjectures of Graffiti","publisher":"University of Auckland; Michael J. Dinneen","url":"https://www.cs.auckland.ac.nz/~mjd/graffiti/info.html","source_class":"OFFICIAL_ORGANIZATION_DATA","publication_date":"1995-12-16","accessed_at":"2026-08-03","claims_supported":["Researchers tested more than 200 Graffiti conjectures using all non-isomorphic graphs through ten vertices.","The effort found counterexamples to several conjectures and also produced some proofs.","Database-backed bounded testing of graph conjectures is longstanding practice rather than a new intervention category."]},{"source_id":"S6","title":"A counterexample to the pseudo 2-factor isomorphic graph conjecture","publisher":"arXiv; Jan Goedgebeur","url":"https://arxiv.org/abs/1412.3350","source_class":"PRIMARY_RESEARCH","publication_date":"2014-12-10","accessed_at":"2026-08-03","claims_supported":["A computer search over generated cubic bipartite graphs found a 30-vertex counterexample to a published conjecture.","The study separately reported finite bounds over which another conjecture survived, without presenting bounded survival as a proof.","Generated-instance counts grew from 125,571 at 30 vertices to more than 57 billion at 40 vertices for the restricted class, demonstrating rapid saturation.","The researchers implemented a conjecture-specific predicate test and published a reconstructable adjacency-list witness."]},{"source_id":"S7","title":"PHOEG: an online tool for discovery and education in extremal graph theory","publisher":"arXiv; University of Mons research team","url":"https://arxiv.org/abs/2603.27242","source_class":"PRIMARY_RESEARCH","publication_date":"2026-03-28","accessed_at":"2026-08-03","claims_supported":["PHOEG is a current web application and API intended to help graph-theory researchers identify conjectures and counterexamples.","It uses a database of pairwise non-isomorphic graphs, including all graphs through order ten.","The paper identifies combinatorial explosion and the exactness-versus-scalability tradeoff as central constraints."]},{"source_id":"S8","title":"Refutation of Spectral Graph Theory Conjectures with Search Algorithms","publisher":"arXiv; Roucairol and Cazenave","url":"https://arxiv.org/abs/2409.18626","source_class":"PRIMARY_RESEARCH","publication_date":"2024-09-27","accessed_at":"2026-08-03","claims_supported":["Exhaustive bounded graph generation is described as a usual approach to finding counterexamples.","The authors identify graph-size limits of exhaustive enumeration and tedious manual invariant evaluation.","Their search-based alternative refuted 12 of 13 previously refuted spectral conjectures in seconds and one then-open Graffiti conjecture, establishing a strong non-enumerative comparator."]}],"problem_evidence":{"support":"STRONG","rationale":"The problem class is visible across decades and remains active in 2026. More than 200 Graffiti conjectures were computationally screened, direct computer searches have refuted published graph conjectures, and current systems explicitly support counterexample discovery. Exhaustive graph counts also grow rapidly enough to make bounds and resource discipline material. What remains unmeasured is the candidate's claimed prevalence of duplicated setup and undocumented testing within any specific research group.","source_ids":["S3","S5","S6","S7","S8"]},"stakeholder_evidence":{"support":"MODERATE","rationale":"Identifiable potential adopters and authorizers include the House of Graphs and PHOEG research teams, graph-theory research groups using their services, and communities represented by the DIMACS working group. These sources express demand for accessible testing and counterexample-discovery systems. No source records a commitment to adopt this particular restricted-grammar, independently validated dossier service or willingness to fund its maintenance.","source_ids":["S3","S4","S7"]},"prior_art":{"proximity":"SUBSTANTIAL_COLLISION","closest_analogues":[{"name":"nauty/geng with SageMath exhaustive graph generators","similarity":"Already supplies reusable canonical or isomorphism-reduced generation, restricted graph-class options, compact representations, and exhaustive traversal—the central substrate stream of the proposal.","remaining_difference":"It does not itself provide conjecture intake semantics, predicate-version governance, independent witness validation, epistemic dossier language, queue stewardship, or comparative turnover measurement.","source_ids":["S1","S2"]},{"name":"House of Graphs 2.0","similarity":"Provides centralized reusable graph corpora, precomputed invariants, searchable counterexample-oriented workflows, complete lists for selected classes, and user-contributed interesting graphs.","remaining_difference":"It searches stored graphs rather than executing a declared universal implication across a versioned canonical stream with per-run resource bounds, independent validators, and immutable coverage dossiers.","source_ids":["S3"]},{"name":"PHOEG","similarity":"A current web service and API using pairwise non-isomorphic graphs to discover exact extremal relationships and counterexamples, including complete coverage through order ten.","remaining_difference":"Its invariant-space and convex-hull workflow is narrower than a general predicate grammar and does not establish the proposed blinded validation, regeneration, queueing, or bounded-reporting protocol.","source_ids":["S7"]},{"name":"Computational attack on Graffiti conjectures","similarity":"Directly reused a corpus of all non-isomorphic graphs through a bound to screen hundreds of graph-invariant conjectures and report counterexamples.","remaining_difference":"The available account does not establish a maintained multi-user intake service, independent implementation, resource-equivalent comparison, incident withdrawal, or standardized no-witness dossier.","source_ids":["S5"]},{"name":"Goedgebeur's exhaustive counterexample search","similarity":"Generated every graph in a restricted class through declared bounds, applied an executable predicate, found and published a reconstructable witness, and separately reported bounded survival.","remaining_difference":"It was conjecture-specific research rather than an amortized cross-conjecture facility with a restricted declarative grammar and measured setup turnover.","source_ids":["S6"]},{"name":"Search-algorithm refutation of spectral conjectures","similarity":"Automates graph construction and predicate evaluation to refute multiple conjectures, with concrete speed results.","remaining_difference":"It is heuristic rather than exhaustive, spectral-specific, and cannot issue the candidate's complete bounded-coverage dossier; it is a strong comparator for witness-finding efficiency.","source_ids":["S8"]}],"distinctive_claim_remaining":"For conjectures faithfully expressible in a fixed finite-simple-graph predicate grammar, an integrated, versioned service combining canonical enumeration, explicit intake and bounds, witness minimization, a genuinely independent validator, immutable coverage dossiers, and withdrawal/replay controls will reduce total encoding-plus-setup-plus-search-plus-validation work relative to equal-resource ad hoc enumeration and conjecture-specific search, while producing no false witnesses or missed witnesses inside declared coverage and preventing bounded survival from being interpreted as proof.","confidence":"HIGH"},"implementation_evidence":{"support":"MODERATE","rationale":"Canonical labeling, non-isomorphic exhaustive generation, restricted graph generation, invariant computation, searchable corpora, APIs, and automated counterexample search are all demonstrated. A bounded archival implementation is technically credible. Unverified elements are faithful coverage of a useful shared predicate grammar, independence of the second validator, reproducible completeness across versions, privacy controls for unpublished conjectures, and operational behavior under combinatorial explosion. The sources also show that predicate restrictions can invalidate completeness and that heuristic search may outperform enumeration for larger witnesses.","source_ids":["S1","S2","S3","S6","S7","S8"]},"scores":{"meaningful_impact":{"score":3,"rationale":"Finding an in-bound counterexample can prevent wasted proof effort and correct the literature, but the frequency and value of such saves in a target organization are not measured.","source_ids":["S5","S6","S8"]},"stakeholder_pull":{"score":3,"rationale":"Active services and an established research community explicitly value quick conjecture testing and counterexample discovery, but no adopter has requested or funded this exact workflow.","source_ids":["S3","S4","S7"]},"incremental_advantage":{"score":2,"rationale":"Most technical functions are established, and no comparative evidence shows that the integrated dossier service beats nauty/Sage scripts, PHOEG/House of Graphs, or conjecture-specific search after encoding and validation labor are included.","source_ids":["S1","S2","S3","S5","S7","S8"]},"distinctiveness_plausibility":{"score":2,"rationale":"The independent-validator, immutable-dossier, withdrawal/replay, and measured-turnover bundle was not found as one service, but the core bounded-falsification pathway substantially collides with established practice.","source_ids":["S1","S3","S5","S6","S7"]},"technical_implementability":{"score":4,"rationale":"All central computational primitives have mature implementations and documented research use. Difficulty lies primarily in semantic coverage, independent validation, and scale rather than basic feasibility.","source_ids":["S1","S2","S3","S6","S7"]},"adoption_authority_feasibility":{"score":4,"rationale":"A research-group steering committee can authorize a non-live archival probe without changing theorem or publication authority. Wider deployment would require data-access, licensing, priority, and confidentiality rules.","source_ids":["S3","S4","S7"]},"evidence_readiness":{"score":3,"rationale":"A blinded archival comparison can be bounded and measured, but it requires assembling trustworthy archived cases, building two implementations, and obtaining operator time unavailable from web evidence.","source_ids":["S5","S6"]},"safety_net_benefit":{"score":4,"rationale":"Independent witness validation, explicit finite bounds, immutable logs, and mandatory non-proof language directly reduce false-witness and false-confidence risks; their effectiveness still requires testing.","source_ids":["S2","S6"]},"scalability":{"score":2,"rationale":"Reuse is plausible for small supported scopes, but exhaustive enumeration grows explosively and alternative search methods can find larger witnesses much faster. Predicate encoding and human interpretation may also become bottlenecks.","source_ids":["S6","S7","S8"]}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Twelve-case blinded archival probe with a fixed small-order graph scope, one wind-tunnel implementation, an ad hoc comparator, independent witness validation, coverage sampling, and a controlled defect/replay exercise.","confidence":"LOW","assumptions":["Uses existing nauty/Sage components rather than writing canonical generation from scratch.","Requires roughly 6–12 person-weeks across graph-theory, software, and validation roles.","Compute remains at workstation or modest cloud-cluster scale."],"source_ids":["S1","S2"]},"initial_deployment_startup":{"band_2026_usd":"50K_TO_250K","scope":"Research-grade restricted predicate grammar, immutable run manifests, generator and validator versioning, witness minimization, regression corpus, access controls, dashboard, and documentation for one graph-theory group.","confidence":"LOW","assumptions":["Supports a deliberately narrow set of relabeling-invariant predicates.","Reuses open graph software and does not certify a new general-purpose generator.","Excludes high-assurance formal verification and large-cluster procurement."],"source_ids":["S1","S2","S3"]},"operational_launch":{"band_2026_usd":"250K_TO_1M","scope":"Multi-user service launch with two independently maintained evaluation paths, security and confidentiality controls, queue operations, incident withdrawal and replay, monitoring, user support, and an initial compute reserve.","confidence":"LOW","assumptions":["Requires approximately 2–4 technical/research staff equivalents during launch.","Supports unpublished conjectures, increasing security and governance work.","Search bounds remain controlled rather than promising arbitrary exhaustive coverage."],"source_ids":["S3","S7"]},"annual_recurring":{"band_2026_usd":"250K_TO_1M","scope":"Staff stewardship, grammar and invariant maintenance, independent-validator upkeep, regression replay, user intake, storage, monitoring, security review, and bounded compute for an active research service.","confidence":"LOW","assumptions":["Maintains at least two-person technical redundancy plus part-time mathematical review.","Compute consumption is metered and hard-capped because enumeration does not scale uniformly.","No revenue or volunteer-maintenance offset is assumed."],"source_ids":["S6","S7","S8"]}},"verified_pipeline_gates":{"externally_supported_problem":{"status":"YES","reason":"Published searches repeatedly found graph-conjecture counterexamples, current tools explicitly target the task, and observed enumeration growth makes bounded testing and resource accounting consequential.","source_ids":["S5","S6","S7","S8"]},"externally_credible_adopter_or_authorizer":{"status":"YES","reason":"House of Graphs, PHOEG, graph-theory research groups, and the DIMACS community are identifiable operators or users of closely related systems. Interest in this exact service remains unverified.","source_ids":["S3","S4","S7"]},"distinct_testable_incremental_claim":{"status":"YES","reason":"The remaining claim is contrastive and measurable against equal-bound ad hoc enumeration and heuristic or conjecture-specific search using total labor, compute, witness correctness, coverage, rejection accuracy, and epistemic-label outcomes.","source_ids":["S1","S2","S5","S7","S8"]},"bounded_next_evidence_step":{"status":"YES","reason":"A twelve-case concealed archival experiment with fixed versions, graph scope, bounds, resources, comparators, and immediate-stop rules is finite, reversible, and capable of falsifying the incremental claim.","source_ids":[]},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"An authorized archival probe makes no live truth or publication decisions and can stop, retract dossiers, preserve logs, and replay after defects. Confidentiality and correlated-validator risks require controls but are not intrinsic stops.","source_ids":["S2","S6"]},"credible_cost_scope_and_range":{"status":"UNCERTAIN","reason":"The scope and staffing assumptions are explicit and the bands are broad, but the eight-source set contains no direct 2026 labor, hosting, security, or procurement benchmark. Combinatorial growth makes compute cost especially case-dependent.","source_ids":["S6","S7","S8"]}},"next_evidence_step":"With one consenting graph-theory group, select twelve archived finite-simple-graph conjectures: four with independently documented witnesses inside a fixed order bound, four documented as surviving that same bound, and four deliberately ineligible statements. Conceal dispositions from operators. Freeze graph conventions, predicate semantics, generator and validator versions, order bounds, compute ceilings, output language, and stop rules. Randomize eligible cases between (A) the integrated wind tunnel and (B) documented ad hoc nauty/Sage enumeration with identical bounds and compute; also run a heuristic or conjecture-specific search as a witness-finding comparator where applicable. A separately authored implementation must validate every witness and audit a precommitted sample of coverage manifests. Measure setup and encoding labor, wall time, compute, graphs examined, correct witness recovery, false witnesses, missed in-bound witnesses, rejection accuracy, incomplete runs, reproducibility, operator interpretation of no-witness dossiers, and maintenance effort. Inject one controlled omission into a non-production generator copy to test detection, withdrawal, repair, and replay. Stop immediately for any released false witness, missed known in-bound witness, unreproducible claimed coverage, undeclared incomplete run, or interpretation of bounded survival as proof. Falsify the incremental-advantage claim if correctness is not perfect in this probe, if fewer than three of four deliberately ineligible cases are correctly rerouted, or if median total resource-equivalent work per eligible case is not at least 25% below the ad hoc baseline without greater compute allocation.","blocking_evidence":["No target-group audit establishes how often proof work begins without comparable bounded screening or how much duplicated setup currently occurs.","No adopter or funder has committed cases, personnel, compute, data access, or ongoing stewardship.","The shared predicate grammar's faithful coverage and per-case encoding burden are unmeasured.","The proposed generator and independent validator have not demonstrated zero missed regression witnesses or reproducible coverage.","The comparative advantage over ad hoc nauty/Sage work, PHOEG/House of Graphs, and heuristic search has not been tested under equal bounds and resources.","Operator compliance with non-proof language and resistance to bounded-survival anchoring require observation.","Confidentiality, priority, licensing, retention, and incident-response arrangements for unpublished conjectures have not been reviewed.","The cost bands lack direct 2026 labor and infrastructure benchmarks."],"research_disposition":"PARTNERED_RESEARCH_PROGRAM","world_novelty_boundary":"This evaluation found substantial prior art for canonical non-isomorphic generation, exhaustive bounded conjecture screening, searchable counterexample databases, invariant-space web tools, and heuristic graph-construction search. It did not find one source documenting the full restricted-grammar, independently implemented validator, immutable coverage dossier, queue stewardship, withdrawal/replay, and measured-turnover bundle. That absence is only a bounded web-search result, not evidence of world novelty. Patentability, freedom to operate, market size, realized impact, and world novelty remain unmeasured.","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_version":0,"controller_recommendation":{"action":"STOP_EMPIRICAL_RESEARCH_NEEDED","repairable":false,"material_progress_observed":true,"progress_targets":["Secure a named graph-theory adopter or authorizer and a written commitment for the twelve-case archival probe.","Audit the partner's recent conjecture workflow to measure prevalence, duplicated setup, accessible finite counterexamples, and current documentation quality.","Freeze a narrow predicate grammar and independently reviewed semantics before seeing case dispositions.","Implement genuinely separate evaluator and validator paths and pass a concealed regression corpus with zero false or missed in-bound witnesses.","Run the equal-bound comparison and meet the precommitted correctness, rerouting, reproducibility, and at-least-25%-work-reduction thresholds.","Demonstrate controlled-defect detection, dossier withdrawal, repair, full replay, and restoration before any live use.","Collect actual staff-time, compute, storage, security, and maintenance costs to replace the low-confidence resource bands.","Obtain confidentiality, licensing, data-retention, authorship/priority, and incident-response approval for unpublished conjectures."],"reason":"Bounded web research confirms a meaningful problem and technically credible components, but also shows substantial collision with established exhaustive-generation, database, and automated-refutation practice. The only defensible remaining advantage is operational: lower total work with exact bounded correctness, independent validation, reproducible coverage, disciplined rejection, and safer epistemic reporting. Those outcomes require partner data, operator observation, two implementations, and comparative execution; they cannot be verified by further web search."},"proposal_index":4}