{ "schemaVersion": "1.6", "slug": "decision-geometry", "title": "Information-optimal anytime certification of triangle-network compatibility", "shortTitle": "Which histories can the data certify?", "url": "https://evidencepress.org/releases/decision-geometry/", "oneLine": "Explicit information geometry gives an anytime-valid route to the complete compatible set—and identifies boundary questions that remain answerable when complete resolution is impossible.", "abstract": "This unrefereed analytic candidate solves the model-restricted information projection for every off-boundary distribution in the open three-leaf Jukes–Cantor triangle-network union. The resulting sequential procedure is pointwise asymptotically optimal for certifying the complete compatible set as the error allowance tends to zero. At model boundaries, local label constancy classifies finite-output questions admitting reliable finite-mean termination. Exact rational acceptance checks accompany the written arguments. The guarantees assume iid observations and the stated evolutionary model; they do not establish biological validity, a unique generating network, formal verification or independent reproduction.", "datePublished": "2026-09-26", "dateModified": "2026-09-26", "version": "1.0.0-candidate", "doi": "10.5281/zenodo.22983737", "doiUrl": "https://doi.org/10.5281/zenodo.22983737", "conceptDoi": "10.5281/zenodo.22983736", "pdfUrl": "https://github.com/ipitchford/decision-geometry/releases/download/v1.0.0-candidate/decision_geometry.pdf", "altPdfUrl": "https://zenodo.org/records/22983737/files/decision_geometry.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/22983737", "repoUrl": "https://github.com/ipitchford/decision-geometry", "releaseUrl": "https://github.com/ipitchford/decision-geometry/releases/tag/v1.0.0-candidate", "markdownUrl": "https://evidencepress.org/releases/decision-geometry/index.md", "bibtexUrl": "https://evidencepress.org/releases/decision-geometry/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/decision-geometry.mp3?v=9acad37422", "imageUrl": "https://evidencepress.org/assets/og/decision-geometry.png?v=8b5e4bb14c", "coverArtUrl": "https://evidencepress.org/assets/art/decision-geometry.svg?v=ccc8700aac", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/decision-geometry.mp3", "name": "Plain-English audio briefing", "description": "OpenAI synthetic voice; communication only.", "transcriptUrl": "https://evidencepress.org/assets/audio/decision-geometry.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed analytic proof candidate. The full eleven-job producer replay passed; exact outputs matched while three numerical reports differed within accepted checks under local library versions. Four semantic and five integrity/optimization rejection controls passed. Written proofs remain separate from finite checks. No independent reproduction, formal verification, authenticated external review, model validation or exhaustive priority claim." }, "assurance": [ { "dimension": "availability", "label": "Availability and archiving", "question": "Is the evidence package publicly retrievable from an archive under a persistent identifier?", "state": "passed", "evidenceUrl": "https://zenodo.org/records/22983737", "note": "All six GitHub and Zenodo assets were fully downloaded and SHA-256 matched to the final local release files. Availability does not validate the mathematics." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Eleven full replay jobs, 174 saved rational receipts, four semantic controls and five integrity/optimization controls passed. Exact and numerical outcomes remain separate." }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No unaffiliated rerun is evidenced; coordinated agents and supplied replay records do not establish independence." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Auxiliary symbolic and exact checks are implementation diversity within the producing workflow." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No proof-assistant verification of the analytic claims." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "The supplied favourable review is retained as a document, not an authenticated external specialist endorsement." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No journal or external venue peer review is claimed." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "partial", "evidenceUrl": "https://github.com/ipitchford/decision-geometry/actions/runs/36277499580", "note": "Full Linux replay with pinned requirements passed at tagged payload cb882301ce23afb05699bd3b99b987cff63cab3a. The local macOS receipt separately records exact agreement and numerical-version differences; PDF build is not hermetic." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted mathematical research and manuscript preparation; exact originating model identities are not asserted", "Producer-side Python exact, symbolic and numerical checks", "Codex publication intake and authoring" ], "humanRole": "Publication authority and supplied materials only; no human scientific contribution is inferred. Scholarly creator remains Anonymous.", "disclosure": "Received reviews, internal replay and publication checks are producer-coordinated evidence, not authenticated external review or independent reproduction." }, "attributionBoundary": null, "problem": { "name": "Complete compatibility-set certification in overlapping triangle-network models", "url": "https://arxiv.org/abs/2606.26673v1" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "The supplied 26September bundle is preserved byte-for-byte under research/. The public edition adds Anonymous, DOI, licence and publication navigation without changing scientific claims. Research assurance and later site-publication readback remain separate. GitHub v1.0.0-candidate and Zenodo22983737 are published; all six assets were downloaded from both services and hash-matched on26September2026.", "grandfatheredAtSchemaVersion": null, "keywords": [ "phylogenetic networks", "information geometry", "sequential inference", "anytime validity", "partial identification", "KL projection", "rational certificates", "Jukes–Cantor model" ], "keyResults": [ "Explicit model-restricted KL information at every off-boundary distribution in the specified open model union, including singleton projections onto tree limits.", "Pointwise delta-to-zero expected-stopping optimality for the complete compatible set, with leading constant 1/I_P(p).", "Finite-output boundary questions admit reliable finite-mean termination exactly when constant on the local family of compatibility sets.", "Outward rational enclosures with the specified precision schedule preserve the leading complete-set stopping constant." ], "reviews": [], "evidencePackage": "Analytic manuscript, exact and symbolic identities, 174 saved rational acceptance receipts, synthetic experiments with censored observations retained, numerical projection diagnostics, preserved review/source history and final rejection controls.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Currie et al. (2026), Semialgebraic conditions for identifying triangles in phylogenetic networks, version 1, Theorems 3.1–3.2: imported model characterisation.", "url": "https://arxiv.org/abs/2606.26673v1", "doi": "10.48550/arXiv.2606.26673" }, { "citation": "Garivier and Kaufmann (2021), Non-asymptotic sequential tests for overlapping hypotheses applied to near optimal arm identification in bandit models, Section 2: one-correct-region precedent.", "url": "https://arxiv.org/abs/1905.03495v2", "doi": "10.48550/arXiv.1905.03495" }, { "citation": "Kaufmann and Koolen (2021), Mixture martingales revisited with applications to sequential tests and confidence intervals, JMLR22(246), Section4: partition-testing and mixture-martingale precedents.", "url": "https://www.jmlr.org/papers/v22/18-798.html", "doi": null }, { "citation": "Genin and Kelly (2017), The topology of statistical verifiability: topological foundations for local statistical questions.", "url": "https://arxiv.org/abs/1707.09378", "doi": "10.48550/arXiv.1707.09378" }, { "citation": "Bhadane et al. (2026), Testing partially-identifiable causal queries using ternary tests: partially identified question precedent.", "url": "https://arxiv.org/abs/2602.23020", "doi": "10.48550/arXiv.2602.23020" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:decision-geometry", "attemptIds": [ "ep-attempt:decision-geometry-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "evidence-assessment" ], "lineageId": null, "accelerationPrimitives": [ "structural-compression", "certificate-first", "partial-identification", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "decision-rule", "description": "Anytime certification of complete and partial compatibility conclusions.", "scope": "Specified open three-leaf Jukes–Cantor triangle-network union; iid observations; pointwise asymptotic complete-set optimality." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "External semialgebraic membership gives compatible labels; model-restricted KL distances and rational lower enclosures feed a simultaneous confidence rule.", "remainingRisks": [ "Model membership and iid assumptions are premises, not certified by the method.", "Universal analytic proofs are not formalised or independently verified.", "Finite experiments do not establish the asymptotic constant." ] }, "humanJudgmentGates": [ "Publication authorisation only; no human scientific contribution or additional review stage is inferred." ], "parentLinks": [ { "relation": "depends-on-claim", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://arxiv.org/abs/2606.26673v1", "inheritedClaim": "Theorems3.1–3.2 characterise the three open triangle-network models and intersections.", "inheritedAssuranceCeiling": "Imported version-pinned mathematical premise, not independently reproved or external validation of this release." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "formalVerification", "specialistReview", "semanticValidation", "noveltyAssessment", "priorityAssessment" ], "nextAction": "Independent reconstruction of the constrained projection, boundary argument and precision-to-stopping bridge.", "claimCeiling": "Unrefereed analytic candidate with producer-side checks only." }, "impactClaims": [ { "id": "decision-geometry-no-impact", "aim": "science", "outcome": "Inspectable model-specific information geometry and decision procedure", "setting": "Producer-coordinated publication", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "No matched comparator.", "estimand": "No impact effect estimated.", "evidenceRefs": [], "registeredDesignRef": null, "independentAssessment": null } ] }, "researchMetrics": { "schemaVersion": "1.0", "policyUrl": "https://evidencepress.org/api/research-metrics-policy.json", "workLedgerUrl": "https://evidencepress.org/api/work-ledger.json", "claimCeiling": "These records describe scoped workflow inputs and outcomes. They support calibration and reference-class construction, but do not by themselves establish research acceleration, theorem correctness, novelty, independent assurance or impact.", "attempts": [ { "attemptId": "ep-attempt:decision-geometry-publication", "status": "active", "resultClass": "pending", "metrics": { "schemaVersion": "1.0", "measurementScope": "publication-only", "scopeBoundary": "Only the remaining publication work from this registration is measured: final package assembly and bounded assurance repairs, GitHub and Zenodo publication, page/media completion, deployment and canonical readback. The mathematical research and all intake, source refresh, provider diagnosis and checks performed before registration are excluded and left-censored. This is not a discovery-time observation, a complete intake-to-publication clock or an acceleration comparison.", "forecast": { "frozenAt": "2026-09-26T22:38:38.525Z", "procedureClass": "remaining-mathematical-candidate-publication", "targetOutcome": "Complete public candidate package on GitHub and Zenodo, with exact asset identities, a conforming Evidence Press page and media, and canonical deployment readback; no promotion to external or formal verification.", "expectedActiveMinutes": 45, "plausibleLowMinutes": 35, "plausibleHighMinutes": 55, "expectedUnattendedWaitMinutes": 20, "referenceClass": { "label": "Procedural decomposition of remaining publication work", "sampleSize": 0, "basis": "Judgment-based planning prior for the remaining tasks, not an empirical benchmark or a historical timing reconstruction." }, "fermiComponents": [ { "component": "Finalize revised package and affected assurance checks", "count": 1, "lowMinutesPerUnit": 8, "centralMinutesPerUnit": 10, "highMinutesPerUnit": 12, "basis": "The supplied candidate and replay materials already exist; only unresolved publication-scope obligations are counted." }, { "component": "Freeze and publish exact GitHub and Zenodo assets", "count": 1, "lowMinutesPerUnit": 7, "centralMinutesPerUnit": 10, "highMinutesPerUnit": 13, "basis": "Provider identities and assets require explicit readback; unattended transfer and CI wait are separate." }, { "component": "Complete page, scientific art, thumbnail and audio QA", "count": 1, "lowMinutesPerUnit": 12, "centralMinutesPerUnit": 15, "highMinutesPerUnit": 18, "basis": "Existing authoring tools; page, informative scientific art and audio remain to be completed." }, { "component": "Seal, deploy, append live observations and close", "count": 1, "lowMinutesPerUnit": 8, "centralMinutesPerUnit": 10, "highMinutesPerUnit": 12, "basis": "Existing two-cycle release contract, with exact bytes and canonical readback; no gate removal." } ], "probabilityPositiveSignal": 0.85, "probabilityTargetClosure": 0.8, "probabilityHorizonMinutes": 120, "assumptions": [ "No fatal proof, integrity or rights defect is found in the affected final checks.", "The authorised providers remain accessible, and existing automation can publish the final candidate assets.", "All claimed assurance remains unrefereed and producer-side unless separately evidenced." ], "reforecastTriggers": [ "A provider or credential failure blocks the relevant publication path.", "A load-bearing defect requires substantive repair beyond packaging.", "Final asset identity or deployment readback fails." ], "stopRule": "A forecast is not a cap. 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