{
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  "slug": "kawasaki-analytic-fast-regimes",
  "title": "Entropy contraction for global Kawasaki dynamics in the analytic fast regimes",
  "shortTitle": "Global swaps, fast mixing",
  "url": "https://evidencepress.org/releases/kawasaki-analytic-fast-regimes/",
  "oneLine": "A candidate entropy proof gives an O(n log n) mixing bound for the original global exchange chain in two strict, source-defined regimes.",
  "abstract": "This unrefereed mathematical candidate gives an O(n log n) worst-start mixing bound for discrete nonlazy global Kawasaki dynamics on bounded-degree graphs in both strict analytic fast regimes of Kuchukova, Pappik, Perkins and Yap. The argument combines mixed-pinning analytic control, sparse localisation, an occupied-bond channel degraded from independent vertex thinning, and a direct entropy contraction for the original chain. A finite binomial retention coefficient and a heterogeneous conditional entropy bridge are included. The latter still assumes an entropic-independence window and does not establish new unconditional inhomogeneous fast regimes. Critical boundaries, nearest-neighbour dynamics, cutoff and practical runtime constants are not claimed.",
  "datePublished": "2026-10-14",
  "dateModified": "2026-10-14",
  "version": "4.0.0-candidate",
  "doi": "10.5281/zenodo.23353348",
  "doiUrl": "https://doi.org/10.5281/zenodo.23353348",
  "conceptDoi": "10.5281/zenodo.23353347",
  "pdfUrl": "https://zenodo.org/records/23353348/files/kawasaki-analytic-fast-regimes-v4.0.0-candidate.pdf",
  "altPdfUrl": "https://github.com/ipitchford/kawasaki-analytic-fast-regimes/releases/download/v4.0.0-candidate/kawasaki-analytic-fast-regimes-v4.0.0-candidate.pdf",
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  "markdownUrl": "https://evidencepress.org/releases/kawasaki-analytic-fast-regimes/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/kawasaki-analytic-fast-regimes/cite.bib",
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      "name": "Audio briefing — Global swaps, fast mixing",
      "description": "Synthetic explanation; not additional scientific evidence.",
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  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
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    "detail": "Unrefereed AI-assisted mathematical candidate. No unaffiliated reproduction, external peer review, formal verification or global priority certification established."
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      "state": "passed",
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      "note": "Published GitHub and Zenodo assets matched the frozen local package by provider digests and downloaded bytes; site readback is recorded separately."
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      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "Supplied finite audits and fresh public diagnostics passed normal and optimized execution; exact identities and floating entropy calculations are distinguished. Universal statements remain written proofs.",
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      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
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      "note": "No unaffiliated reproduction established."
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      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "No independent reimplementation established."
    },
    {
      "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 established."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "Internal model checks do not establish external specialist review."
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    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
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    },
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      "dimension": "dataEnvironmentReproducibility",
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      "state": "partial",
      "evidenceUrl": "https://github.com/ipitchford/kawasaki-analytic-fast-regimes/blob/v4.0.0-candidate/ENVIRONMENT.txt",
      "note": "Python standard-library diagnostics and version information supplied. No hermetic reconstruction or unaffiliated reproduction established."
    }
  ],
  "provenance": {
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    "aiAssisted": true,
    "generatedBy": [
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    "humanRole": "Publication authority; no human mathematical contribution asserted.",
    "reviewStatus": "Coordinated internal proof and finite diagnostic checks; no external peer review."
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  "attributionBoundary": null,
  "problem": {
    "name": "Global Kawasaki mixing in the strict analytic fast regimes",
    "url": "https://arxiv.org/abs/2405.06209v2"
  },
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  "corrections": [],
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  "recordMaturity": "current",
  "metadataProvenance": "Revised manuscript, archive-bound replay and scoped internal proof checks, 14 October 2026; public availability is assessed separately.",
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  "keywords": [
    "Kawasaki dynamics",
    "Ising model",
    "Markov-chain mixing",
    "entropy contraction",
    "entropic independence",
    "independent thinning",
    "bounded-degree graphs"
  ],
  "keyResults": [
    "For fixed degree, inverse temperature and magnetisation in either strict KPPY fast regime, the original discrete nonlazy global Kawasaki chain has candidate O(n log n) worst-start mixing.",
    "A common vertex-thinning to occupied-bond channel yields entropy retention within an extensive positive-pinning window.",
    "Corollary 4 retains a finite binomial coefficient with fixed-parameter limit (1−q)^C.",
    "Corollary 5 extends the abstract bridge to unequal nonnegative interactions conditional on the same entropic-independence window."
  ],
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  "evidencePackage": "Written proof with coordinated internal finite audits. Exact channel, transition-kernel and pinning identities are distinguished from numerical entropy calculations; neither establishes the universal theorem by enumeration.",
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  "relatedWorks": [
    {
      "citation": "Kuchukova, Pappik, Perkins and Yap, Fast and Slow Mixing of Kawasaki Dynamics on Bounded-Degree Graphs, arXiv:2405.06209v2. Source problem, exact analytic thresholds and canonical inputs.",
      "url": "https://arxiv.org/abs/2405.06209v2",
      "doi": "10.48550/arXiv.2405.06209"
    },
    {
      "citation": "Jain, Pham and Vuong, Entropic independence via sparse localization, arXiv:2604.10902v1. Sparse-localisation input.",
      "url": "https://arxiv.org/abs/2604.10902v1",
      "doi": "10.48550/arXiv.2604.10902"
    },
    {
      "citation": "Cryan, Guo and Mousa, Modified log-Sobolev inequalities for strongly log-concave distributions, arXiv:1903.06081. Weighted-slice deletion inequality.",
      "url": "https://arxiv.org/abs/1903.06081",
      "doi": "10.48550/arXiv.1903.06081"
    },
    {
      "citation": "Cohen and coauthors, Relative entropy under mappings by stochastic matrices, Linear Algebra and its Applications 179 (1993), 211–235. Relative-entropy coefficient input.",
      "url": "https://doi.org/10.1016/0024-3795(93)90331-H",
      "doi": "10.1016/0024-3795(93)90331-H"
    },
    {
      "citation": "Chen, Ju, Miao, Yin and Zhang, Edge-Tilting Field Dynamics: Rapid Mixing at the Uniqueness Threshold and Optimal Mixing for Swendsen–Wang Dynamics, arXiv:2604.10525v2. Prior occupied-edge augmentation and interaction cancellation.",
      "url": "https://arxiv.org/abs/2604.10525v2",
      "doi": "10.48550/arXiv.2604.10525"
    },
    {
      "citation": "Blanca, Caputo, Parisi, Sinclair and Vigoda, Entropy decay in the Swendsen–Wang dynamics on Z^d, arXiv:2007.06931v2. Earlier auxiliary spin–bond entropy methods.",
      "url": "https://arxiv.org/abs/2007.06931v2",
      "doi": "10.48550/arXiv.2007.06931"
    }
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