{"schema_version":1,"research_id":"eoa_inverse_innovation_exp06_external_evaluation_20260803","source_assessment_id":"representation_independent_interface_contract__mathematics:P4:v0","cell_id":"representation_independent_interface_contract__mathematics","search_queries":["uniform random labeled graph versus unlabeled graph isomorphism classes probability measure sampling paper","official documentation random graph G(n,p) labeled vertices seed reproducibility NetworkX","nauty geng non-isomorphic graphs official user guide","NumPy random reproducibility seed stream compatibility policy NEP 19","Fosdick Larremore Nishimura Ugander configuring random graph models fixed degree sequences labeling conclusions SIAM Review PDF","official NetworkX gnp_random_graph each possible edge probability p documentation source","SageMath random_gnp uniform graph p=1/2 documentation","computational mathematics reproducibility guidelines official journal code data","uniform random unlabeled graph automorphism class size labeled graphs paper","sampling unlabeled graphs uniformly isomorphism classes software official","uniform generation of random graphs labeled unlabeled automorphism group probability","graph enumeration geng exactly one graph each isomorphism class official","site:siam.org reproducibility computational results code data policy authors","site:ams.org mathematics journal computational experiments code reproducibility policy","site:acm.org artifact review reproducibility computational experiments official policy","ICERM reproducibility computational experimental mathematics report recommendations"],"sources":[{"source_id":"S1","title":"Configuring Random Graph Models with Fixed Degree Sequences","publisher":"arXiv; subsequently SIAM Review","url":"https://arxiv.org/abs/1608.00607","source_class":"PRIMARY_RESEARCH","publication_date":"2018","accessed_at":"2026-08-03","claims_supported":["Uniform random-graph models require an explicit graph space and labeling convention.","Different model choices produced substantial differences in conclusions in three reported applications.","This paper's specific stub-labeled versus vertex-labeled distinction was inconsequential for simple graphs, so it is supporting context rather than direct proof of the candidate's labeled-versus-isomorphism-class example."]},{"source_id":"S2","title":"Uniform Generation of Unlabelled Graphs","publisher":"Journal of Combinatorial Mathematics and Combinatorial Computing / Combinatorial Press","url":"https://combinatorialpress.com/jcmcc-articles/volume-063/uniform-generation-of-unlabelled-graphs/","source_class":"PRIMARY_RESEARCH","publication_date":"2007-11-30","accessed_at":"2026-08-03","claims_supported":["Uniform labeled graphs are generated by independently selecting every possible edge with probability one half.","Uniform generation over unlabeled graphs is a separate and materially less straightforward sampling problem.","The candidate's labeled-versus-unlabeled population distinction is established prior art."]},{"source_id":"S3","title":"gnp_random_graph — NetworkX 3.6.1 documentation","publisher":"NetworkX","url":"https://networkx.org/documentation/stable/reference/generated/networkx.generators.random_graphs.gnp_random_graph.html","source_class":"OFFICIAL_PRODUCT_DOCUMENTATION","publication_date":"undated; version 3.6.1 documentation","accessed_at":"2026-08-03","claims_supported":["NetworkX already exposes a public G(n,p) sampling model in which each possible edge is chosen with probability p.","At p=1/2 this realizes the candidate's uniform measure over labeled simple graphs.","The API explicitly accepts an RNG-state indicator and rejects unsupported multigraph types."]},{"source_id":"S4","title":"Random graphs — SageMath Graph Theory documentation","publisher":"SageMath","url":"https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/generators/random.html","source_class":"OFFICIAL_PRODUCT_DOCUMENTATION","publication_date":"undated; current documentation","accessed_at":"2026-08-03","claims_supported":["SageMath defines RandomGNP by independent edge insertion with probability p.","One semantic operation can select either Sage's implementation or NetworkX algorithms, directly demonstrating representation- and algorithm-level substitution behind a shared distributional description.","The same documentation warns that another named random-regular-bipartite implementation is not uniform, showing that uniformity must be specified rather than inferred from a random-graph return type."]},{"source_id":"S5","title":"nauty and Traces User's Guide, Version 2.9.3","publisher":"Australian National University / nauty project","url":"https://users.cecs.anu.edu.au/~bdm/nauty/nug29.pdf","source_class":"OFFICIAL_PRODUCT_DOCUMENTATION","publication_date":"Version 2.9.3; undated","accessed_at":"2026-08-03","claims_supported":["The graph6 format maps the upper triangle of a labeled simple graph's adjacency matrix to a bit vector of length n(n-1)/2 with a declared edge order.","The geng utility generates all graphs in a specified class, while genrang generates random graphs with selectable edge probability and seed.","These established tools make exhaustive small-n enumeration, independent encoding, complementation, relabeling, and oracle construction technically straightforward."]},{"source_id":"S6","title":"NEP 19 — Random Number Generator Policy","publisher":"NumPy","url":"https://numpy.org/neps/nep-0019-rng-policy.html","source_class":"OFFICIAL_GUIDANCE","publication_date":"2019-05-21","accessed_at":"2026-08-03","claims_supported":["Exact seed-to-stream compatibility was pursued for reproducibility but impeded algorithmic improvement.","A seed alone does not guarantee identical results across builds, platforms, versions, or downstream transformations.","NumPy recommends pinning the complete software environment when bit-for-bit replay is required and distinguishes stable low-level streams from higher-level distribution semantics."]},{"source_id":"S7","title":"SIAM Journal on Scientific Computing — Editorial Policy","publisher":"Society for Industrial and Applied Mathematics","url":"https://epubs.siam.org/journal/sisc/editorial-policy","source_class":"OFFICIAL_GUIDANCE","publication_date":"current policy accessed 2026-08-03","accessed_at":"2026-08-03","claims_supported":["SIAM identifies independent reproducibility as a core principle of computational research.","SISC strongly encourages permanent deposition of software, data, setup information, and post-processing details.","Authors must answer reviewer inquiries about reproducibility, identifying journal editors and reviewers as credible external authorizers."]},{"source_id":"S8","title":"Setting the Default to Reproducible: Reproducibility in Computational and Experimental Mathematics","publisher":"Institute for Computational and Experimental Research in Mathematics, Brown University","url":"https://icerm.brown.edu/topical_workshops/tw12-5-rcem/icerm_report.pdf","source_class":"OFFICIAL_GUIDANCE","publication_date":"2013-02-16","accessed_at":"2026-08-03","claims_supported":["Computational and experimental mathematicians reported difficulty verifying findings under prevailing computational practices.","The workshop recommended integrating reproducibility into research and called on journals, funders, and employers to support it.","The report distinguishes recreating results from numerical reproducibility and independent repetition, supporting the candidate's distinction between measure-level substitution and exact replay."]}],"problem_evidence":{"support":"STRONG","rationale":"The mathematical issue is real and directly visible: independently choosing the binomial(n,2) labeled edges at p=1/2 is uniform over 2^binomial(n,2) labeled graphs, whereas uniformly choosing an unlabeled isomorphism class and then a labeling weights labeled outcomes through class-orbit sizes. S2 expressly distinguishes these two populations; S1 shows that ambiguous random-graph spaces can affect conclusions; and S6 verifies that seed streams are implementation- and environment-scoped. The prevalence of the exact failure in a particular experimental graph-theory project was not externally measured.","source_ids":["S1","S2","S6","S8"]},"stakeholder_evidence":{"support":"MODERATE","rationale":"Credible authorizers are identifiable: the responsible mathematicians and sampler maintainers have local authority, while SIAM editors and reviewers explicitly demand enough computational detail to assess reproducibility. ICERM participants, including experimental mathematicians, journals, funders, and laboratories, expressed the broader need. No named graph-theory project or maintainer was found asking specifically for this proposed contract package.","source_ids":["S7","S8"]},"prior_art":{"proximity":"ESTABLISHED_PRACTICE","closest_analogues":[{"name":"G(n,p) model APIs in NetworkX and SageMath","similarity":"They already define random graphs by the probability law that independently includes each labeled edge, and SageMath permits distinct backends under that semantic description.","remaining_difference":"The documentation does not present the candidate's full package of an opaque sampler type, exact small-n cross-implementation oracle, leakage audit, typed replay scope, and predeclared event analysis.","source_ids":["S3","S4"]},{"name":"Uniform labeled versus uniform unlabeled graph generation","similarity":"The research literature explicitly treats uniform labeled and uniform unlabeled generation as different sampling problems and gives algorithms for each.","remaining_difference":"The literature establishes the population distinction but does not itself evaluate whether the proposed software-contract workflow improves one experimental project's error detection or maintenance.","source_ids":["S1","S2"]},{"name":"nauty graph6, geng, and genrang toolchain","similarity":"It supplies a canonical labeled adjacency-bit encoding, exhaustive graph generation, random graph generation, relabeling, complementation, and seed controls—most of the proposed pilot machinery.","remaining_difference":"It is a toolchain rather than the proposed host-project governance contract and does not make one seed portable between unrelated sampler implementations.","source_ids":["S5"]},{"name":"NumPy RNG compatibility policy","similarity":"It explicitly separates distribution correctness and algorithmic evolution from exact stream replay, documenting why seed-level compatibility can freeze implementation choices.","remaining_difference":"It governs general numerical RNG infrastructure, not the probability measure and abstract observations of finite labeled graphs.","source_ids":["S6"]}],"distinctive_claim_remaining":"The only potentially distinctive claim is workflow-level: in one host experiment, a common measure contract plus an independently derived exhaustive oracle and leakage audit will detect more consequential weighting, replay, or representation dependencies than the host's existing model prose, saved outputs, and per-implementation tests. The candidate's stated edge-bit-versus-rank-decoder equality is testable but is largely a direct consequence of the established G(n,1/2) definition, not a demonstrated incremental advantage.","confidence":"HIGH"},"implementation_evidence":{"support":"STRONG","rationale":"For n=4 and n=5 the complete labeled spaces contain only 64 and 1,024 graphs, respectively. Existing official tools specify the adjacency-bit mapping and exhaustive generation, while NetworkX and Sage already implement the target G(n,p) semantics with different algorithm paths. The pilot requires no sensitive data, regulated decision, network service, or production-user exposure. Remaining technical uncertainties concern independence assumptions, unbiased bounded-integer generation, entropy exhaustion, shared-code defects, and whether the oracle genuinely remains independent.","source_ids":["S3","S4","S5","S6"]},"scores":{"meaningful_impact":{"score":4,"rationale":"Using the wrong probability space can invalidate exploratory frequencies and, in documented random-graph applications, model choices can change conclusions. The immediate affected population is nevertheless a bounded class of computational graph experiments.","source_ids":["S1","S2"]},"stakeholder_pull":{"score":3,"rationale":"Experimental-mathematics organizations and SIAM express strong general reproducibility demand, but no particular graph project requested this exact intervention.","source_ids":["S7","S8"]},"incremental_advantage":{"score":2,"rationale":"The contract consolidates useful safeguards, but G(n,p) semantics, multiple backends, exhaustive encodings, graph generators, and scoped RNG compatibility are already established. No comparison demonstrates superiority over a concise population statement plus preserved samples and conventional tests.","source_ids":["S2","S3","S4","S5","S6"]},"distinctiveness_plausibility":{"score":1,"rationale":"The central mathematical and software ideas substantially collide with established literature, APIs, enumeration formats, and RNG policy. Only the integrated governance presentation may differ, and world novelty remains unmeasured.","source_ids":["S2","S3","S4","S5","S6"]},"technical_implementability":{"score":5,"rationale":"The target measure is elementary, the proposed finite spaces are tiny, and mature libraries and formats already implement the needed semantics and enumerations.","source_ids":["S3","S4","S5"]},"adoption_authority_feasibility":{"score":4,"rationale":"A project's mathematicians and maintainers can authorize an isolated pilot without statutory approval, and journal reproducibility policy supports the workflow. A specific willing host has not been identified.","source_ids":["S7","S8"]},"evidence_readiness":{"score":4,"rationale":"The proposed n=4/n=5 test, predeclared events, independent encodings, and biased mutant yield immediate exact evidence. What is missing is a real host baseline and observed downstream representation dependence.","source_ids":["S4","S5"]},"safety_net_benefit":{"score":4,"rationale":"The intervention is reversible, preserves existing samplers and datasets, and can reveal silent population changes before conclusions are affected. It cannot establish that labeled-uniform sampling is scientifically appropriate or turn sampling evidence into proof.","source_ids":["S1","S7"]},"scalability":{"score":3,"rationale":"The semantic contract applies at arbitrary n, but exhaustive conformance scales as 2^binomial(n,2). Large-n assurance therefore depends on proofs, carefully justified transformations, mutation tests, and statistical diagnostics rather than complete enumeration.","source_ids":["S2","S3","S5"]}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"UNDER_10K","scope":"One researcher implements the two deliberately independent n=4/n=5 samplers, exhaustive oracle, eight frozen events, relabeling/complement checks, and one biased mutant over roughly one to two work weeks.","confidence":"MODERATE","assumptions":["Existing open-source graph and test tooling is reused.","Only 1,088 labeled graph states are exhaustively processed across n=4 and n=5.","No production integration, procurement, or external audit is included."],"source_ids":["S4","S5"]},"initial_deployment_startup":{"band_2026_usd":"10K_TO_50K","scope":"Harden the contract and harness, independently review the probability mapping and RNG premises, add typed failures and replay metadata, document versioning, and integrate one research codebase.","confidence":"MODERATE","assumptions":["Approximately one to three person-months of research-software and mathematical-review effort.","The existing experiment has ordinary source control and automated testing.","No redesign of unrelated graph analyses is required."],"source_ids":["S3","S4","S5","S6"]},"operational_launch":{"band_2026_usd":"10K_TO_50K","scope":"Audit downstream dependencies, migrate analyses to abstract edge observations, archive samples or environment-scoped replay bundles, run the full predeclared experiment, and complete independent reproducibility review.","confidence":"LOW","assumptions":["One moderate-sized experimental project is in scope.","Archived datasets remain unchanged.","The number of downstream scripts and hidden representation dependencies is not known."],"source_ids":["S6","S7","S8"]},"annual_recurring":{"band_2026_usd":"UNDER_10K","scope":"Maintain contract tests, replay/version metadata, dependency pins, documentation, and review of sampler changes for a single small project.","confidence":"LOW","assumptions":["Few sampler changes occur annually.","Existing continuous-integration infrastructure is available.","No long-term support for many historical RNG implementations is promised."],"source_ids":["S6","S7"]}},"verified_pipeline_gates":{"externally_supported_problem":{"status":"YES","reason":"Primary research and official RNG policy support both population-definition ambiguity and seed-stream fragility; the exact labeled-versus-unlabeled distinction is directly established.","source_ids":["S1","S2","S6"]},"externally_credible_adopter_or_authorizer":{"status":"YES","reason":"SIAM editors and reviewers are credible external authorizers for reproducibility evidence, and ICERM identifies experimental mathematicians, journals, funders, and employers as stakeholders. Willingness of a particular host project remains unverified.","source_ids":["S7","S8"]},"distinct_testable_incremental_claim":{"status":"NO","reason":"Exact agreement between edge-bit and rank-decoder implementations is bounded and falsifiable but follows from the established G(n,1/2) model. The genuinely incremental workflow claim—better detection than prose, stored outputs, or ordinary tests—lacks a comparator design and predeclared detection metric.","source_ids":["S2","S3","S4","S5"]},"bounded_next_evidence_step":{"status":"YES","reason":"Complete enumeration at n=4 and n=5, frozen events, two independent encodings, all relabelings, complementation, repeated-state checks, and a biased mutant form a small, finite, reversible test with explicit falsifiers.","source_ids":["S4","S5"]},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"An isolated, non-conclusion-bearing software pilot involves no regulated data or external users; project mathematicians retain interpretation authority, and journal policy supports independent review.","source_ids":["S7","S8"]},"credible_cost_scope_and_range":{"status":"YES","reason":"The first-evidence computation is tiny and supported by mature open-source tooling. Broader deployment costs are scoped by person-time and explicitly marked low-confidence where the host codebase is unknown.","source_ids":["S4","S5","S6"]}},"next_evidence_step":"If a host project wants quality assurance, pre-register a two-arm diagnostic over its existing baseline and the proposed contract workflow. Freeze n in {4,5}, the labeled-uniform law, RNG premises, failure policy, eight graph events, and a defect set containing at least: uniform-isomorphism-class weighting, modulo-biased rank selection, outcome-selective exhaustion, storage-order dependence, portable-seed assumptions, and shared observation-code corruption. Have one team implement independent edge bits and another implement integer-rank decoding with a different edge order and storage type. Exhaust all 64 and 1,024 ranks; compare per-graph and per-event counts to a separately generated graph6/geng oracle; apply every vertex permutation and complement; and verify repeated draws separately. Comparator: the host's current prose, saved-output, and test workflow receives the same seeded defects. Primary incremental endpoint: proportion of predeclared consequential defects rejected before analysis. Falsifiers: any candidate implementation passes the proposed oracle while inducing a different exact event probability, the proposed workflow detects no more consequential defects than baseline, the oracle shares the defect it is intended to detect, or the host already has equivalent measure-level checks and representation-independent analyses.","blocking_evidence":["No external evidence establishes how often the exact labeled-versus-isomorphism-class mistake occurs in computational graph-theory projects.","No named host project has demonstrated storage-order dependence, seed-portability assumptions, or willingness to adopt the package.","The candidate has not compared defect-detection yield, maintenance effort, or researcher error against a concise population statement plus preserved abstract samples and conventional testing.","No large-n proof obligation or validation design has been supplied for rank selection, buffered entropy, rejection behavior, and successive-sample independence.","World novelty, patentability, freedom to operate, market size, and realized impact are unmeasured."],"research_disposition":"KNOWN_PRACTICE_DIFFUSION","world_novelty_boundary":"This evaluation found established labeled and unlabeled random-graph models, G(n,p) APIs with alternative backends, exact adjacency-bit encodings and exhaustive generators, and explicit RNG stream-compatibility policy. It did not conduct a comprehensive literature, patent, repository, or product search for the exact combined contract-and-conformance package. World novelty, patentability, freedom to operate, market size, and realized impact remain unmeasured.","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_version":0,"controller_recommendation":{"action":"STOP_DIFFUSION","repairable":false,"material_progress_observed":true,"progress_targets":["Reframe the proposal as a practical diffusion and quality-assurance pattern built from established G(n,p), graph-enumeration, and RNG-reproducibility practices.","Do not present edge-bit versus rank-decoder equivalence or labeled-versus-unlabeled population separation as a novel research contribution.","Identify a willing host experiment and document actual representation leaks before allocating deployment resources.","If comparative evidence is desired, predeclare defect mutants and measure detection yield against the host's current workflow rather than merely showing that two correct implementations agree.","Preserve sampled abstract graphs or a pinned full environment when exact replay is required; treat distribution-level substitutability as a separate objective."],"reason":"The problem is genuine, technically easy to test, and supported by credible reproducibility authorizers, but the core intervention substantially matches established mathematical models, software APIs, graph encodings, enumeration tools, and RNG policy. The bounded pilot is suitable as adoption-quality work, not as a distinct opportunity claim. The missing evidence is comparative field evidence from a real host, while bounded web research has already resolved the prior-art question sufficiently for diffusion disposition."},"proposal_index":4}