{ "schemaVersion": "1.6", "slug": "potts-censoring-counterexample", "title": "A five-vertex counterexample to ferromagnetic Potts censoring", "shortTitle": "Skipping one Potts update", "url": "https://evidencepress.org/releases/potts-censoring-counterexample/", "oneLine": "An exact five-vertex example shows that omitting one predetermined update can leave a ferromagnetic three-colour Potts model closer to equilibrium at a fixed horizon.", "abstract": "This anonymous unrefereed candidate gives a finite-horizon counterexample to the universal ferromagnetic Potts censoring inequality from a monochromatic start. On a five-vertex six-edge graph with three colours, no external fields and uniform activity 30, deleting the seventh update from a nine-opportunity heat-bath word strictly reduces total-variation distance to the full Gibbs law. The positive gap is an exact rational, approximately 1.0319815176e-8. A written reduction to 27 marginal entries, three producer-side exact reconstructions, complete final distributions and adversarial controls are supplied. Exact supplementary checks explain the reversal after a common suffix and certify a longer all-sites-updated witness. No mixing-time improvement, practical speed-up, minimality, historical priority or external validation is claimed.", "datePublished": "2026-09-06", "dateModified": "2026-09-06", "version": "0.1.0-candidate", "doi": "10.5281/zenodo.22546547", "doiUrl": "https://doi.org/10.5281/zenodo.22546547", "conceptDoi": "10.5281/zenodo.22546546", "pdfUrl": "https://github.com/ipitchford/potts-censoring-counterexample/releases/download/v0.1.0-candidate/potts-censoring-counterexample-0.1.0-candidate.pdf", "altPdfUrl": "https://zenodo.org/records/22546547/files/potts-censoring-counterexample-0.1.0-candidate.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/22546547", "repoUrl": "https://github.com/ipitchford/potts-censoring-counterexample", "releaseUrl": "https://github.com/ipitchford/potts-censoring-counterexample/releases/tag/v0.1.0-candidate", "markdownUrl": "https://evidencepress.org/releases/potts-censoring-counterexample/index.md", "bibtexUrl": "https://evidencepress.org/releases/potts-censoring-counterexample/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/potts-censoring-counterexample.mp3?v=e8f20f6426", "imageUrl": "https://evidencepress.org/assets/og/potts-censoring-counterexample.png?v=951a4677ef", "coverArtUrl": "https://evidencepress.org/assets/art/potts-censoring-counterexample.svg?v=95f6f83e0c", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/potts-censoring-counterexample.mp3", "name": "Audio briefing — skipping one Potts update", "description": "Plain-English synthetic narration; communication, not additional evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/potts-censoring-counterexample.txt" }, { "type": "video", "url": "https://youtu.be/oLS684sjZX4", "name": "The Rule and the Anomaly", "description": "Evidence Press video overview of this release. This is a communication aid; it does not extend the release's claims or assurance status and is not additional research evidence." } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed exact finite-horizon q=3 counterexample candidate. No mixing-time, random-scan, every-q, minimality, practical speed-up, exhaustive novelty, priority, unaffiliated validation, formal proof or impact 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/22546547", "note": "Public GitHub and Zenodo assets were independently downloaded and hashed against the local frozen files." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Three producer-side exact implementations, supplemental trajectory and all-sites witness, 14 test groups in normal and optimized modes, fresh extraction and hosted Python CI. Five internal AI editorial roles accept; no external assurance promotion.", "evidenceUrl": "https://github.com/ipitchford/potts-censoring-counterexample/blob/v0.1.0-candidate/replay-receipt.json" }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No authenticated unaffiliated evidence establishes this dimension. Producer-coordinated implementations and internal AI review do not qualify." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "No authenticated unaffiliated evidence establishes this dimension. Producer-coordinated implementations and internal AI review do not qualify." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No authenticated unaffiliated evidence establishes this dimension. Producer-coordinated implementations and internal AI review do not qualify." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "No authenticated unaffiliated evidence establishes this dimension. Producer-coordinated implementations and internal AI review do not qualify." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No authenticated unaffiliated evidence establishes this dimension. Producer-coordinated implementations and internal AI review do not qualify." }, { "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/potts-censoring-counterexample/blob/v0.1.0-candidate/ENVIRONMENT.md", "note": "Standard-library exact replay, source inputs and hashes supplied; no hermetic environment or cross-platform PDF identity claim." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "OpenAI Codex under human direction", "Python standard library", "XeLaTeX / TeX Live 2026" ], "humanRole": "Research direction, problem selection, supplied review and publication authorization; scholarly creator remains Anonymous.", "disclosure": "AI assistance produced research, proof exposition, code, revisions, internal editorial review and packaging. No unaffiliated assurance follows from multiple coordinated programs or reviewers." }, "attributionBoundary": null, "problem": { "name": "AIM-PROBABILITY-0035: Censoring for the Potts model", "url": "https://www.unsolvedmath.com" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Research assurance assessed 2026-09-06T17:16:56.806Z against the frozen mathematical target and its identity-bearing successor. Internal editorial review and producer replay do not promote external assurance. Canonical publication readback and terminal metrics are separate later events.", "grandfatheredAtSchemaVersion": null, "keywords": [ "Potts model", "censoring inequality", "heat-bath dynamics", "total variation", "exact counterexample", "unrefereed candidate" ], "keyResults": [ "A predetermined interior update deletion strictly reduces finite-horizon total-variation distance for the specified ferromagnetic q=3 monochromatic-start model.", "Exact 243-state laws reduce to 27 marginal rows with the full unconditioned Gibbs reference.", "The extra update initially helps; relative distance ordering reverses after the shared suffix.", "A separate activity-100 supporting witness updates every site in both words." ], "reviews": [], "evidencePackage": "Six-page DOI-bearing paper, aligned mathematical Markdown, exact distributions and marginal certificate, three producer-side exact implementations, supplemental exact trajectory and all-sites witness, 14 adversarial test groups, normal/optimized and fresh-extraction replay, hosted Python CI, a supplied-review response, five frozen internal editorial reports and synthesis, source comparison and component licences. Public assets match across GitHub, Zenodo and local hashes. Internal editorial decision: https://github.com/ipitchford/potts-censoring-counterexample/blob/v0.1.0-candidate/editorial/DECISION.md.", "openProblems": [ "Obtain an unaffiliated reconstruction and authenticated specialist review.", "Determine smaller graphs or shorter schedules; no minimality was proved.", "Find explicit activity intervals and assess other colour counts.", "Identify structural conditions controlling relative-distance reversal without inferring mixing-time or practical gains." ], "mathObjects": [], "relatedWorks": [ { "citation": "Peres and Winkler (2013). Can extra updates delay mixing? Monotone-system positive theorem.", "url": "https://doi.org/10.1007/s00220-013-1776-0", "doi": "10.1007/s00220-013-1776-0" }, { "citation": "Holroyd (2011). Some circumstances where extra updates can delay mixing. Antiferromagnetic failure and ferromagnetic constant-start question.", "url": "https://doi.org/10.1007/s10955-011-0365-x", "doi": "10.1007/s10955-011-0365-x" }, { "citation": "Fill and Kahn (2013). Comparison inequalities and fastest-mixing Markov chains.", "url": "https://doi.org/10.1214/12-AAP886", "doi": "10.1214/12-AAP886" }, { "citation": "Blanca and Tahmidur (2026). Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model. Different asymptotic setting.", "url": "https://arxiv.org/abs/2607.09841", "doi": "10.48550/arXiv.2607.09841" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:potts-censoring-counterexample", "attemptIds": [ "ep-attempt:potts-censoring-counterexample-assurance-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "evidence-assessment", "communication" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "structural-compression", "adversarial-controls", "counterexample-proxy-first", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "counterexample", "description": "Explicit finite ferromagnetic Potts heat-bath update word and exact positive distance gap.", "scope": "q=3, five vertices, activity 30, monochromatic start and one fixed nine-opportunity comparison." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Neighbour-count heat-bath probabilities, full Gibbs-fibre reconstruction and conditional-factor marginal reduction target the same finite state laws and predetermined deletion.", "remainingRisks": [ "Same-producer implementation and semantic errors remain possible.", "No proof-assistant certification.", "Inaccessible original AIM endpoint; bounded priority search.", "No broader mixing-time or practical consequence established." ] }, "humanJudgmentGates": [ "Check the source-to-state-law and unconditioned-equilibrium bridge.", "Preserve finite-horizon scope and distinguish contraction from relative ordering.", "Assess priority separately from exact correctness.", "Preserve rights, Anonymous authorship and assurance separation." ], "parentLinks": [ { "relation": "depends-on-claim", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://arxiv.org/abs/1101.4690", "inheritedClaim": "Primary text poses the ferromagnetic constant-start censoring question.", "inheritedAssuranceCeiling": "Historical question framing, not a proof or current priority clearance." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "independentReimplementation", "formalVerification", "specialistReview", "semanticValidation", "noveltyAssessment", "priorityAssessment" ], "nextAction": "Seek unaffiliated exact reconstruction and specialist assessment; treat extensions as new research.", "claimCeiling": "Unrefereed exact finite-horizon q=3 counterexample candidate. No mixing-time, random-scan, every-q, minimality, practical speed-up, exhaustive novelty, priority, unaffiliated validation, formal proof or impact claim." }, "impactClaims": [ { "id": "potts-censoring-counterexample-no-impact", "aim": "science", "outcome": "Reusable exact censoring obstruction", "setting": "Producer-coordinated mathematical candidate publication", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "No matched workflow comparator.", "estimand": "No discovery, effort, reuse or 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:potts-censoring-counterexample-assurance-publication", "status": "published", "resultClass": "positive", "metrics": { "schemaVersion": "1.0", "measurementScope": "assurance-through-publication", "scopeBoundary": "Prospective supplemental assurance and publication only. The exact discovery, supplied review, and initial wording/documentation edits predate registration and are excluded; no historical discovery clock is reconstructed.", "forecast": { "frozenAt": "2026-09-06T17:03:07.016Z", "procedureClass": "minor-revision-assurance-full-candidate", "targetOutcome": "Supplemental exact checks, complete package and PDF, five-role internal editorial gate, public GitHub and Zenodo archives, media and two guarded publication cycles.", "expectedActiveMinutes": 120, "plausibleLowMinutes": 80, "plausibleHighMinutes": 180, "expectedUnattendedWaitMinutes": 20, "referenceClass": { "label": "Evidence Press full-candidate procedure", "sampleSize": 1, "basis": "Procedural reference only; not a calibrated comparative sample." }, "fermiComponents": [ { "component": "Exact supplements, packaging and PDF", "count": 1, "lowMinutesPerUnit": 20, "centralMinutesPerUnit": 30, "highMinutesPerUnit": 45, "basis": "Existing written proof and three exact checkers." }, { "component": "Five-role editorial gate", "count": 1, "lowMinutesPerUnit": 15, "centralMinutesPerUnit": 25, "highMinutesPerUnit": 40, "basis": "Frozen target and bounded differentiated roles." }, { "component": "Immutable identities, page and media", "count": 1, "lowMinutesPerUnit": 25, "centralMinutesPerUnit": 35, "highMinutesPerUnit": 50, "basis": "Established generators and authenticated services." }, { "component": "Two deployment cycles and closeout", "count": 1, "lowMinutesPerUnit": 20, "centralMinutesPerUnit": 30, "highMinutesPerUnit": 45, "basis": "Required new-slug A/B and C/D cycles." } ], "probabilityPositiveSignal": 0.95, "probabilityTargetClosure": 0.85, "probabilityHorizonMinutes": 180, "assumptions": [ "Exact witnesses replay.", "Authenticated publishing services available.", "No critical editorial finding." ], "reforecastTriggers": [ "Scientific or rights defect.", "Authentication failure.", "Concurrent site conflict." ], "stopRule": "Fail closed on scientific, rights, CI or public-byte-integrity failures; no expansion of the mathematical claim." }, "outcome": { "measuredAt": "2026-09-06T17:33:47.585Z", "calendarElapsedMinutes": 31, "activeAgentMinutes": 5, "activeHumanMinutes": null, "computeMinutes": null, "unattendedWaitMinutes": 4, "blockedMinutes": 0, "reworkMinutes": 1, "agentRuns": 6, "maxParallelAgents": 4, "modelTurns": 6, "deduplicatedModelTokens": 12260070, "uncachedInputTokens": 532071, "researchCycles": { "positive": 0, "negative": 0, "inconclusive": 0 }, "falsificationGatesRun": 1, "candidateArchitecturesTested": 0, "candidateArchitecturesRejected": 0, "substantiveReviewRounds": 1, "p0Findings": 0, "p1Findings": 0, "prepublicationClaimCorrections": 0, "resultState": "positive-signal", "resultSummary": "Exact supplemental assurance, five internal Accept reports, immutable GitHub/Zenodo identity and the first canonical Evidence Press release passed. No new discovery cycle is claimed. The frozen target also includes the second ledger-sealing deployment, still pending at this immutable measurement cut; final Git/CI/deployment receipts establish that later event separately.", "positiveSignalObserved": true, "targetReached": false, "forecastErrorMinutes": -115, "forecastRatio": 0.041666666666666664, "withinForecastInterval": false, "varianceReason": "Generation and context-compaction wait are observed lower bounds, not complete labour or wait totals. Rework is an upper attribution bound on coordinator generation during the first failed site-build to repaired-content build window. Token scope uses response-completion timestamps; a boundary-crossing response may include some pre-registration input. Cached input is included in raw tokens and separated below. No acceleration inference. This first-publication cut is narrower than the forecast full closeout; no performance or forecast-success conclusion follows.", "missingFields": [ { "field": "activeHumanMinutes", "reason": "No contemporaneous human active-time telemetry." }, { "field": "computeMinutes", "reason": "No complete resource-time accounting for all local and hosted checks." } ] } }, "missingnessReason": null } ] } }