{
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  "slug": "two-class-transposition-profiles",
  "title": "Exact profiles and a vanishing-bias crossover for two-class random transpositions",
  "shortTitle": "Two counts describe the remaining shuffle",
  "url": "https://evidencepress.org/releases/two-class-transposition-profiles/",
  "oneLine": "A candidate full-law profile for a two-class biased shuffle, including the crossover as bias vanishes.",
  "abstract": "For independent label sampling in two equal classes, this unrefereed candidate approximates the full permutation density by a normalized tilt in the two class-specific fixed-point counts. It gives exact limiting total-variation profiles for fixed bias and every vanishing-bias crossover, including infinity. A separate uniform spectral tail bridges the parameter regimes. Finite exact checks corroborate specified identities only.",
  "datePublished": "2026-09-12",
  "dateModified": "2026-09-12",
  "version": "0.1.0-candidate",
  "doi": "10.5281/zenodo.22727156",
  "doiUrl": "https://doi.org/10.5281/zenodo.22727156",
  "conceptDoi": "10.5281/zenodo.22727155",
  "pdfUrl": "https://github.com/ipitchford/two-class-transposition-profiles/releases/download/v0.1.0-candidate/two-class-transposition-profiles-0.1.0-candidate.pdf",
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  "repoUrl": "https://github.com/ipitchford/two-class-transposition-profiles",
  "releaseUrl": "https://github.com/ipitchford/two-class-transposition-profiles/releases/tag/v0.1.0-candidate",
  "markdownUrl": "https://evidencepress.org/releases/two-class-transposition-profiles/index.md",
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  "authors": [
    "Anonymous"
  ],
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  "status": "unrefereed-candidate",
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    "independentlyReproduced": false,
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    "detail": "Unrefereed equal-class, identity-start full-density and TV profile candidate. Finite checks do not certify asymptotics. No uniformity as b tends to zero, unequal-class extension, external validation, formal verification, priority or impact claim."
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      "question": "Is the evidence package publicly retrievable from an archive under a persistent identifier?",
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      "evidenceUrl": "https://zenodo.org/records/22727156",
      "note": "Public archive bytes checked before site deployment."
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      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "Finite exact identities and semantic controls, not asymptotic certification.",
      "evidenceUrl": "https://github.com/ipitchford/two-class-transposition-profiles/blob/v0.1.0-candidate/REPLAY_RECEIPT.md"
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      "dimension": "independentRerun",
      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
      "state": "not-assessed",
      "note": "Internal model reports and supplied evidence do not establish this external assurance dimension."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "Internal model reports and supplied evidence do not establish this external assurance dimension."
    },
    {
      "dimension": "formalVerification",
      "label": "Formal verification",
      "question": "Is a formalised statement machine-checked, and over which trusted base?",
      "state": "not-assessed",
      "note": "Internal model reports and supplied evidence do not establish this external assurance dimension."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "Internal model reports and supplied evidence do not establish this external assurance dimension."
    },
    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
      "note": "Internal model reports and supplied evidence do not establish this external assurance dimension."
    },
    {
      "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/two-class-transposition-profiles/blob/v0.1.0-candidate/README.md",
      "note": "Standard-library replay with Linux CI; diagnostic environment pinned; PDF build not hermetic."
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  "provenance": {
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    "aiAssisted": true,
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    "humanRole": "Research direction, supplied reviews and full publication authority; scholarly creator Anonymous.",
    "disclosure": "Internal model review and supplied-review checks do not establish unaffiliated mathematical validation."
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  "problem": {
    "name": "Two-class biased random-transposition profile and vanishing-bias crossover",
    "url": "https://arxiv.org/abs/2409.16387v1"
  },
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  "keywords": [
    "random transpositions",
    "cutoff profile",
    "vanishing bias",
    "Littlewood–Richardson",
    "mixing times"
  ],
  "keyResults": [
    "Stationary-L2 approximation of the full permutation density by a two-count tilt.",
    "Fixed-bias full total-variation profile from the slow-class fixed points.",
    "Two-Poisson crossover at bias scale 1/log N, including both endpoints.",
    "Asymptotic conditional sufficiency, not exact finite-size sufficiency."
  ],
  "reviews": [],
  "evidencePackage": "Fourteen-page complete candidate paper; normal and optimized exact checks; rejected semantic mutants; scoped supplied spectral checks; source crosswalk; five producer-coordinated internal editorial reports; file manifest.",
  "openProblems": [
    "Unequal or additional sampling classes require new estimates.",
    "Bias tending to zero lies outside the uniform theorem.",
    "Quantitative finite-size conditional-sufficiency errors remain open.",
    "Transfer the norm-saturation mechanism to other noncentral walks."
  ],
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  "relatedWorks": [
    {
      "citation": "Nestoridi and Yan, Cutoff for the Biased Random Transposition Shuffle, arXiv:2409.16387v1: spectrum and fixed-bias bulk input.",
      "url": "https://arxiv.org/abs/2409.16387v1",
      "doi": "10.48550/arXiv.2409.16387"
    },
    {
      "citation": "Anonymous, Untouched subsets and a counterexample to the biased-transposition limit-profile conjecture, Evidence Press (2026): antecedent lower-bound obstruction.",
      "url": "https://doi.org/10.5281/zenodo.22708622",
      "doi": "10.5281/zenodo.22708622"
    },
    {
      "citation": "Teyssier, Limit profile for random transpositions (2020): uniform endpoint.",
      "url": "https://doi.org/10.1214/20-AOP1424",
      "doi": "10.1214/20-AOP1424"
    },
    {
      "citation": "Teyssier, Cutoff profiles for conjugacy invariant random walks on symmetric groups, arXiv:2605.28770v2 (2026): related central-character framework.",
      "url": "https://arxiv.org/abs/2605.28770v2",
      "doi": "10.48550/arXiv.2605.28770"
    },
    {
      "citation": "Jain and Sawhney, Hitting time mixing for the random transposition walk (2026): planted fixed-set comparison.",
      "url": "https://doi.org/10.1007/s00440-026-01479-9",
      "doi": "10.1007/s00440-026-01479-9"
    },
    {
      "citation": "Francis and Nestoridi, Limit Profiles for Separation Distance, arXiv:2605.19084v1 (2026): different metric and singleton-class perturbation.",
      "url": "https://arxiv.org/abs/2605.19084v1",
      "doi": "10.48550/arXiv.2605.19084"
    }
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      "remainingRisks": [
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        "Bounded source search does not establish priority."
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