{ "schemaVersion": "1.6", "slug": "rfim-unbounded-fields-entropy", "title": "Modified log-Sobolev inequalities for the random field Ising model with unbounded fields", "shortTitle": "Entropy decay without a field ceiling", "url": "https://evidencepress.org/releases/rfim-unbounded-fields-entropy/", "oneLine": "Sign-adapted localisation controls continuous-time entropy decay and mixing under strong disorder, without an upper bound on finite field strengths.", "abstract": "This unrefereed mathematical candidate proves a field-uniform Dirichlet-form modified log-Sobolev inequality for heat-bath Glauber dynamics on arbitrary finite bounded-degree graphs under a strong-disorder anti-concentration hypothesis. Sign-adapted localisation leaves opposite-preference strong-field edges interacting, and controls the resulting low-activity endpoint. A site-covering warm-up gives field-tail-free continuous-time total-variation mixing on the same high-probability event. Independent nonidentically distributed field magnitudes are also covered under a common small-field bound. One-step entropy contraction and approximate tensorization are not established; explicit constants can be very large.", "datePublished": "2026-10-18", "dateModified": "2026-10-18", "version": "1.0.0", "doi": "10.5281/zenodo.23452100", "doiUrl": "https://doi.org/10.5281/zenodo.23452100", "conceptDoi": "10.5281/zenodo.23452099", "pdfUrl": "https://github.com/ipitchford/rfim-unbounded-fields-entropy/releases/download/v1.0.0/rfim-unbounded-fields-entropy.pdf", "altPdfUrl": null, "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23452100", "repoUrl": "https://github.com/ipitchford/rfim-unbounded-fields-entropy", "releaseUrl": "https://github.com/ipitchford/rfim-unbounded-fields-entropy/releases/tag/v1.0.0", "markdownUrl": "https://evidencepress.org/releases/rfim-unbounded-fields-entropy/index.md", "bibtexUrl": "https://evidencepress.org/releases/rfim-unbounded-fields-entropy/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/rfim-unbounded-fields-entropy.mp3", "imageUrl": "https://evidencepress.org/assets/og/rfim-unbounded-fields-entropy.png?v=86e5fd7883", "coverArtUrl": "https://evidencepress.org/assets/art/rfim-unbounded-fields-entropy.svg?v=ae42bfd993", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/rfim-unbounded-fields-entropy.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/rfim-unbounded-fields-entropy.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed AI-assisted candidate. Continuous-time Dirichlet-form entropy decay, not one-step contraction. No external peer review or formal verification established." }, "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/23452100", "note": "Full public downloads of manuscript PDF, research ZIP and checksum manifest from GitHub and Zenodo matched frozen local bytes. Archiving does not establish mathematical correctness." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Four revised numerical diagnostics and 11 regression tests in ordinary and optimised Python passed. Finite sampled cases and bounded local optimization are diagnostic only; rejected optimizer starts are explicit. No global search, certified lower bound or independent reproduction is established.", "evidenceUrl": "https://github.com/ipitchford/rfim-unbounded-fields-entropy/blob/v1.0.0/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": "Not established by this producer-coordinated workflow." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Not established by this producer-coordinated 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 formalisation established." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "No external specialist review established." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "Internal model assessment is not external peer review." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "not-assessed", "note": "Finite mathematical checks do not establish empirical data reproducibility." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted research workflow", "OpenAI Codex: checking, revision and publication" ], "humanRole": "Publication authority only; no human research contribution inferred.", "reviewStatus": "Internal AI-assisted assessment, not external peer review." }, "attributionBoundary": null, "problem": { "name": "Unbounded-field entropy inequalities for the random field Ising model", "url": "https://arxiv.org/abs/2605.02002v1" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Prepared from the revised version 1.0.0 manuscript, research commit d1892668a811428749284881bba542b894f57350. Full GitHub and Zenodo downloads of PDF, ZIP and checksum manifest matched the frozen local bytes on 18 October 2026. Research ZIP SHA-256 c67fb599d26dc35a3b9d4ce9edd5bbea87f249e93f94ebcc99759b36683705fa.", "grandfatheredAtSchemaVersion": null, "keywords": [ "random field Ising model", "modified log-Sobolev inequality", "Glauber dynamics", "entropy decay", "localisation", "strong disorder" ], "keyResults": [ "A field-uniform continuous-time entropy-decay bound holds with probability 1 − O(1/n) under the stated independent-magnitude anti-concentration hypothesis.", "Sign-adapted localisation retains strong opposite-preference edges; the endpoint is not a product measure.", "A known site-covering warm-up yields O(n^(1+c) log(n/epsilon)) mixing on the same event without a field-tail assumption; the explicit exponent may be large." ], "reviews": [], "evidencePackage": "Written analytic proof with finite computational checks of selected identities and endpoint estimates; computations are not the universal proof.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Han (2026), Glauber dynamics for random field Ising models on bounded degree graphs and MLSI. Version 1.", "url": "https://arxiv.org/abs/2605.02002v1", "doi": "10.48550/arXiv.2605.02002" }, { "citation": "Niles-Weed (2026), Reweighted information inequalities. Known heat-bath mixture comparison.", "url": "https://arxiv.org/abs/2603.13135v1", "doi": "10.48550/arXiv.2603.13135" }, { "citation": "Wang (2026), Optimal Mixing of Glauber Dynamics for the Sherrington–Kirkpatrick Model at beta < 1/2. Version 2, Lemma 4.4.", "url": "https://arxiv.org/abs/2608.22159v2", "doi": "10.48550/arXiv.2608.22159" }, { "citation": "Caputo, Chen, Gu and Polyanskiy (2025), Entropy contractions in Markov chains: Half-step, full-step and continuous-time.", "url": "https://doi.org/10.1214/25-EJP1372", "doi": "10.1214/25-EJP1372" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:rfim-unbounded-fields-entropy", "attemptIds": [ "ep-attempt:rfim-unbounded-fields-entropy-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "communication" ], "lineageId": null, "accelerationPrimitives": [ "structural-compression", "research-lineage-reuse", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "bound", "description": "Field-uniform continuous-time entropy and mixing bounds.", "scope": "Independent finite field magnitudes under common strong-disorder anti-concentration; not one-step contraction." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "One total heat-bath update per unit time; Dirichlet-form entropy decay is distinct from one-step contraction.", "remainingRisks": [ "Analytic proof is not formally verified.", "Finite checks do not prove unrestricted entropy inequalities." ] }, "humanJudgmentGates": [ "Publication authorised; external specialist assessment remains open." ], "parentLinks": [ { "relation": "depends-on-claim", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://arxiv.org/abs/2605.02002v1", "inheritedClaim": "Disagreement-percolation and localisation architecture under anti-concentration.", "inheritedAssuranceCeiling": "Source-dependent analytic argument; no external review inferred." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "specialistReview", "formalVerification", "priorityAssessment" ], "nextAction": "Unaffiliated analytic proof scrutiny and supporting-check replay.", "claimCeiling": "Independent finite field magnitudes under common strong-disorder anti-concentration; not one-step contraction. 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