{
  "schemaVersion": "1.6",
  "slug": "biased-transposition-profile-counterexample",
  "title": "Untouched subsets and a counterexample to the biased-transposition limit-profile conjecture",
  "shortTitle": "A shuffle profile fails the subset test",
  "url": "https://evidencepress.org/releases/biased-transposition-profile-counterexample/",
  "oneLine": "Two slow fixed labels force a total-variation lower bound above the conjectured profile.",
  "abstract": "In a shuffle with two equally sized probability classes, an event involving the slow class yields an asymptotic distance of at least 0.710647716, above the conjectured 0.681595297. The candidate disproves the formula in Nestoridi–Yan arXiv v1 and gives general deterministic-subset lower bounds. It supplies no replacement profile or matching general upper bound.",
  "datePublished": "2026-09-11",
  "dateModified": "2026-09-11",
  "version": "1.0.1-candidate",
  "doi": "10.5281/zenodo.22708622",
  "doiUrl": "https://doi.org/10.5281/zenodo.22708622",
  "conceptDoi": "10.5281/zenodo.22708621",
  "pdfUrl": "https://github.com/ipitchford/biased-transposition-profile-counterexample/releases/download/v1.0.1-candidate/biased-transposition-profile-counterexample-1.0.1-candidate.pdf",
  "altPdfUrl": "https://zenodo.org/records/22708622/files/biased-transposition-profile-counterexample-1.0.1-candidate.pdf?download=1",
  "altPdfLabel": null,
  "zenodoUrl": "https://zenodo.org/records/22708622",
  "repoUrl": "https://github.com/ipitchford/biased-transposition-profile-counterexample",
  "releaseUrl": "https://github.com/ipitchford/biased-transposition-profile-counterexample/releases/tag/v1.0.1-candidate",
  "markdownUrl": "https://evidencepress.org/releases/biased-transposition-profile-counterexample/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/biased-transposition-profile-counterexample/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/biased-transposition-profile-counterexample.mp3?v=dc33c03caf",
  "imageUrl": "https://evidencepress.org/assets/og/biased-transposition-profile-counterexample.png?v=b0018d92a5",
  "coverArtUrl": "https://evidencepress.org/assets/art/biased-transposition-profile-counterexample.svg?v=08d86a7a64",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/biased-transposition-profile-counterexample.mp3",
      "name": "Plain-English audio briefing",
      "description": "OpenAI synthetic voice; communication only.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/biased-transposition-profile-counterexample.txt"
    }
  ],
  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
  "verification": {
    "peerReviewed": false,
    "independentlyReproduced": false,
    "formallyVerified": false,
    "internallyReplayed": true,
    "detail": "Unrefereed candidate. Internal model review and producer replay support inspection; formal verification, external reproduction, external peer review and priority remain unestablished. No replacement profile or general t_mix = t_star + O(n) upper bound is supplied."
  },
  "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/22708622",
      "note": "Exact public archive bytes checked before deployment."
    },
    {
      "dimension": "internalReplay",
      "label": "Internal replay",
      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "Exact inequalities, eight 61-row trajectories and 23 hostile controls; no formal proof of the asymptotic argument.",
      "evidenceUrl": "https://github.com/ipitchford/biased-transposition-profile-counterexample/blob/v1.0.1-candidate/REPLAY_RECEIPT.md"
    },
    {
      "dimension": "independentRerun",
      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
      "state": "not-assessed",
      "note": "Producer-coordinated replay only."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "The alternate implementation belongs to the producing process."
    },
    {
      "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."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "No unaffiliated specialist review recorded."
    },
    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
      "note": "Model-assisted internal review only."
    },
    {
      "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/biased-transposition-profile-counterexample/blob/v1.0.1-candidate/ENVIRONMENT.txt",
      "note": "Pinned numerical dependency, normal/optimized local replay and Linux CI."
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "OpenAI Codex under human direction",
      "Python exact arithmetic and finite replay",
      "Pandoc and Tectonic"
    ],
    "humanRole": "Research selection, supplied review, direction and publication authorization; scholarly creator Anonymous.",
    "disclosure": "AI-assisted manuscript, software, internal editorial review and publication. Supplied review authorship and external independence are unestablished."
  },
  "attributionBoundary": null,
  "problem": null,
  "orderedProductAverage": null,
  "corrections": [],
  "publicCorrections": [],
  "publicCorrectionIndexes": null,
  "pageStructureVersion": "2.0",
  "pageStructureVariant": "canonical-theorem",
  "pageStructureWaivers": [],
  "recordMaturity": "current",
  "metadataProvenance": "Internal review and finite replay are separate from public availability and external scientific validation.",
  "grandfatheredAtSchemaVersion": null,
  "keywords": [
    "random transpositions",
    "limit profile",
    "total variation",
    "Markov chains",
    "counterexample",
    "untouched labels"
  ],
  "keyResults": [
    "For every fixed 0 < b < 1, the equal-half conjectured profile fails at s = log(6).",
    "The event of at least two fixed slow labels gives B0 = 0.710647716… > D0 = 0.681595297….",
    "An exact finite-moment witness supplies a second unconditional contradiction.",
    "A deterministic-subset Poisson argument gives general one-sided lower bounds."
  ],
  "reviews": [],
  "evidencePackage": "Written proofs, exact arithmetic contract, 23 hostile controls, finite-state replay and five internal role reports plus bounded confirmation and deterministic closure. https://github.com/ipitchford/biased-transposition-profile-counterexample/blob/v1.0.1-candidate/EDITORIAL_DECISION.md",
  "openProblems": [
    "Determine a replacement limit profile.",
    "Establish a matching upper bound at the untouched-label centre for general bounded product weights.",
    "Obtain external scrutiny of the written proof and contribution-specific novelty."
  ],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Nestoridi and Yan (2024), Cutoff for the biased random transposition shuffle, arXiv v1: Conjecture 1.6 is the precise target.",
      "url": "https://arxiv.org/abs/2409.16387v1",
      "doi": "10.48550/arXiv.2409.16387"
    },
    {
      "citation": "Nestoridi and Yan (2025), FPSAC proceedings article: cutoff and spectrum results, distinct from the profile conjecture.",
      "url": "https://www.mat.univie.ac.at/~slc/wpapers/FPSAC2025/6.pdf",
      "doi": null
    },
    {
      "citation": "Nestoridi and Yan, official FPSAC 2025 poster: restates the profile conjecture.",
      "url": "https://www.math.sci.hokudai.ac.jp/sympo/fpsac2025/public/posters/107.pdf",
      "doi": null
    },
    {
      "citation": "Teyssier (2020), Limit profile for random transpositions: the uniform-shuffle benchmark.",
      "url": "https://doi.org/10.1214/20-AOP1424",
      "doi": "10.1214/20-AOP1424"
    },
    {
      "citation": "Evidence Press (2026), Biased shuffles still cut off: related bounded-product cutoff candidate.",
      "url": "https://evidencepress.org/releases/bounded-product-transposition-cutoff/",
      "doi": null
    }
  ],
  "claimAssurance": null,
  "operatingModel": {
    "version": "1.0",
    "workId": "ep-work:biased-transposition-profile-counterexample",
    "attemptIds": [
      "ep-attempt:biased-transposition-profile-counterexample-assurance-publication"
    ],
    "aims": [
      "science"
    ],
    "artifactRoles": [
      "research-output",
      "evidence-assessment"
    ],
    "lineageId": null,
    "accelerationPrimitives": [
      "structural-compression",
      "research-lineage-reuse",
      "adversarial-controls",
      "assurance-vector",
      "agent-readable-research-object"
    ],
    "decisionObject": {
      "type": "counterexample",
      "description": "An observable-event contradiction to a specified limit-profile formula.",
      "scope": "Equal-half product-weight transpositions, fixed 0 < b < 1, s = log(6)."
    },
    "bottleneckTargeted": [
      "assurance",
      "publication"
    ],
    "semanticBridge": {
      "state": "explicit",
      "description": "Untouched slow labels imply fixed slow labels; event probability differences bound full total variation.",
      "remainingRisks": [
        "Written asymptotic argument awaits external scrutiny.",
        "Priority search is bounded."
      ]
    },
    "humanJudgmentGates": [
      "Inspect the asymptotic moment argument and source correspondence.",
      "Assess novelty and retain candidate qualifications."
    ],
    "parentLinks": [
      {
        "relation": "depends-on-claim",
        "workId": null,
        "legacyReleaseSlug": null,
        "externalUrl": "https://arxiv.org/abs/2409.16387v1",
        "inheritedClaim": "The stated equal-half profile conjecture and model conventions define the target.",
        "inheritedAssuranceCeiling": "The source conjecture is a target, not a proved input or external validation."
      }
    ],
    "assuranceTarget": {
      "dimensions": [
        "independentRerun",
        "formalVerification",
        "specialistReview",
        "semanticValidation",
        "noveltyAssessment",
        "priorityAssessment"
      ],
      "nextAction": "Obtain external probability-specialist inspection and replay.",
      "claimCeiling": "Candidate counterexample to the pinned profile formula; no replacement profile or general sharp upper bound."
    },
    "impactClaims": [
      {
        "id": "biased-transposition-profile-counterexample-no-impact",
        "aim": "science",
        "outcome": "Inspectable candidate counterexample",
        "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:biased-transposition-profile-counterexample-assurance-publication",
        "status": "published",
        "resultClass": "positive",
        "metrics": {
          "schemaVersion": "1.0",
          "measurementScope": "assurance-through-publication",
          "scopeBoundary": "Remaining confirmation and publication after registration; discovery, supplied review, first review round and initial repairs excluded. The 150-minute route prior was recorded in publication state at 12:12:30Z before this ledger registration; decomposition is a procedural prior, not measured research effort.",
          "forecast": {
            "frozenAt": "2026-09-11T12:18:19Z",
            "procedureClass": "repaired-candidate-publication",
            "targetOutcome": "Close deterministic confirmation findings and complete GitHub, Zenodo, media and guarded public site readback.",
            "expectedActiveMinutes": 150,
            "plausibleLowMinutes": 120,
            "plausibleHighMinutes": 210,
            "expectedUnattendedWaitMinutes": 30,
            "referenceClass": {
              "label": "Full-candidate route prior",
              "sampleSize": 0,
              "basis": "Existing publication-state prior; no empirical speed claim."
            },
            "fermiComponents": [
              {
                "component": "Remaining assurance and archive",
                "count": 1,
                "lowMinutesPerUnit": 40,
                "centralMinutesPerUnit": 50,
                "highMinutesPerUnit": 70,
                "basis": "Bounded confirmation and deterministic repairs."
              },
              {
                "component": "Page and communication assets",
                "count": 1,
                "lowMinutesPerUnit": 40,
                "centralMinutesPerUnit": 50,
                "highMinutesPerUnit": 70,
                "basis": "Established site generators."
              },
              {
                "component": "CI, deployment and public readback",
                "count": 1,
                "lowMinutesPerUnit": 40,
                "centralMinutesPerUnit": 50,
                "highMinutesPerUnit": 70,
                "basis": "Two standard seal and deployment cycles."
              }
            ],
            "probabilityPositiveSignal": 0.9,
            "probabilityTargetClosure": 0.8,
            "probabilityHorizonMinutes": 300,
            "assumptions": [
              "No new scientific blocker.",
              "Provider credentials permit publication."
            ],
            "reforecastTriggers": [
              "Provider or integrity failure."
            ],
            "stopRule": "Resolve integrity defects; timing forecast is telemetry and not a publication cap."
          },
          "outcome": {
            "measuredAt": "2026-09-11T12:55:33.385Z",
            "calendarElapsedMinutes": 37,
            "activeAgentMinutes": 9,
            "activeHumanMinutes": null,
            "computeMinutes": null,
            "unattendedWaitMinutes": 0,
            "blockedMinutes": 0,
            "reworkMinutes": 0,
            "agentRuns": 2,
            "maxParallelAgents": 2,
            "modelTurns": 148,
            "deduplicatedModelTokens": 19095439,
            "uncachedInputTokens": 349927,
            "researchCycles": {
              "positive": 0,
              "negative": 0,
              "inconclusive": 0
            },
            "falsificationGatesRun": 23,
            "candidateArchitecturesTested": 1,
            "candidateArchitecturesRejected": 0,
            "substantiveReviewRounds": 0,
            "p0Findings": 0,
            "p1Findings": 3,
            "prepublicationClaimCorrections": 0,
            "resultState": "target-closed",
            "resultSummary": "Repaired candidate published with exact public archive parity, internal replay, CI, media and canonical site readback; no external verification, priority or replacement profile claimed.",
            "positiveSignalObserved": true,
            "targetReached": true,
            "forecastErrorMinutes": -141,
            "forecastRatio": 0.06,
            "withinForecastInterval": false,
            "varianceReason": "Active minutes are the floored union of observable model-output spans, a strict lower bound excluding initial latency and tools, not an acceleration estimate. Tokens deduplicate response receipts across root and confirmation reviewer, including cached input. Registration excludes discovery, supplied review, initial five-role review and substantive repairs, and also excludes the first three minutes of confirmation. Zero wait, blocked and rework minutes mean no separately metered intervals, not absence of provider waits or repair work. The scoped interval has one bounded confirmation, three packaging P1 findings and no new scientific P0/P1; substantiveReviewRounds is zero because the initial round predates registration. Twenty-three hostile controls test the existing candidate; no new research architecture search. Outcome ends at first successful public readback; administrative ledger reseal and redeployment follow.",
            "missingFields": [
              {
                "field": "activeHumanMinutes",
                "reason": "Human effort was not instrumented."
              },
              {
                "field": "computeMinutes",
                "reason": "Tool and compute execution were not separately metered."
              }
            ]
          }
        },
        "missingnessReason": null
      }
    ]
  }
}