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  "slug": "field-uniform-spin-chains",
  "title": "When no local field can restore a conservation law",
  "shortTitle": "Field-uniform spin-chain obstruction",
  "url": "https://evidencepress.org/releases/field-uniform-spin-chains/",
  "oneLine": "An exact three-site test rules out a range of local conservation laws for every choice of on-site fields—and gives a sharp boundary for a central spin-1 family.",
  "abstract": "For a fixed Hermitian swap-symmetric nearest-neighbour interaction satisfying leading rigidity, a finite quotient removes all on-site fields and two-site corrections from the three-site almost-conservation equations. A nonzero obstruction excludes exact contiguous charge ranges 3 through floor(N/2), for every periodic N ≥ 6 and arbitrary site-dependent Hermitian fields. Multiplicity-free symmetry evaluates the quotient for the spin-1 bilinear–biquadratic family, giving the exact factor u(u−v)(u+v). The candidate also identifies the residual local commutant and certifies two families missed by a cheaper partial-trace test.",
  "datePublished": "2026-09-28",
  "dateModified": "2026-09-28",
  "version": "1.0.1-candidate",
  "doi": "10.5281/zenodo.23021227",
  "doiUrl": "https://doi.org/10.5281/zenodo.23021227",
  "conceptDoi": "10.5281/zenodo.23021226",
  "pdfUrl": "https://github.com/ipitchford/field-uniform-spin-chains/releases/download/v1.0.1-candidate/paper.pdf",
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  "repoUrl": "https://github.com/ipitchford/field-uniform-spin-chains",
  "releaseUrl": "https://github.com/ipitchford/field-uniform-spin-chains/releases/tag/v1.0.1-candidate",
  "markdownUrl": "https://evidencepress.org/releases/field-uniform-spin-chains/index.md",
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      "name": "When No Local Field Can Restore A Conservation Law",
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  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
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    "detail": "Unrefereed candidate with producer-side replay. Universal arguments are not formally verified, and the supplied review is not authenticated external peer review. Quotient consistency is not general integrability; no thermalisation, chaos or quasilocal-charge exclusion is claimed."
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      "evidenceUrl": "https://zenodo.org/records/23021227",
      "note": "All six release assets fully downloaded from GitHub and Zenodo and hash-matched to the frozen inventory on 28 September 2026."
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      "note": "Eight local finite suites passed, including portable witnesses and sixteen corruption controls."
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      "note": "No unaffiliated rerun is evidenced; coordinated agents and supplied replay records do not establish independence."
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      "question": "Is a formalised statement machine-checked, and over which trusted base?",
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      "note": "No proof-assistant verification of the analytic claims."
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      "state": "partial",
      "note": "Clean-extraction macOS replay and exact-commit pinned Linux CI passed. Optimization controls test legacy refusal and explicit witnesses, not optimized legacy mathematics; PDF toolchain is not hermetic.",
      "evidenceUrl": "https://github.com/ipitchford/field-uniform-spin-chains/actions/runs/36461431144"
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    "disclosure": "Received reviews, internal replay and publication checks are producer-coordinated evidence, not authenticated external review or independent reproduction."
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  "attributionBoundary": null,
  "problem": {
    "name": "Can arbitrary on-site fields restore strictly local conservation?",
    "url": "https://arxiv.org/abs/2501.18400v3"
  },
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  "keywords": [
    "quantum spin chains",
    "local conserved quantities",
    "nonintegrability",
    "bilinear-biquadratic model",
    "exact certificates",
    "symmetry averaging"
  ],
  "keyResults": [
    "An exact quotient decides three-site almost-conservation; nonzero obstruction excludes all specified higher-range charges uniformly in fields.",
    "In the spin-1 BLBQ family, some fields admit such a charge exactly on u=0, u=v or u=−v, apart from the zero interaction; zero fields suffice there.",
    "Off these lines the range-bounded local commutant is identity, energy and uniform spin generators commuting with every field.",
    "Exact certificates cover deficient cases and two blind hypersurfaces of the earlier partial-trace obstruction."
  ],
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  "evidencePackage": "Written proofs, exact symbolic identities and modular minors, eight finite suites, portable rational witnesses and tamper controls.",
  "openProblems": [],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Hokkyo (2025), Rigorous test for quantum integrability and nonintegrability, v3: Theorems 1 and 2 supply the range-three reduction, with explicit interaction hypotheses.",
      "url": "https://arxiv.org/abs/2501.18400v3",
      "doi": "10.48550/arXiv.2501.18400"
    },
    {
      "citation": "Shiraishi and Yamaguchi (2026), Dichotomy theorem separating complete integrability and nonintegrability of isotropic spin chains: the closest zero-field symmetry-based predecessor.",
      "url": "https://doi.org/10.1103/lcn4-tbcm",
      "doi": "10.1103/lcn4-tbcm"
    },
    {
      "citation": "Hokkyo, Yamaguchi and Chiba (2025), Absence of nontrivial local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions: includes uniform uniaxial anisotropic fields, not arbitrary site-dependent matrices.",
      "url": "https://doi.org/10.1103/vjtq-sz21",
      "doi": "10.1103/vjtq-sz21"
    },
    {
      "citation": "Park and Lee (2024), Proof of nonintegrability of the spin-1 bilinear-biquadratic chain model: independent antecedent for the zero-field classification.",
      "url": "https://arxiv.org/abs/2410.23286",
      "doi": "10.48550/arXiv.2410.23286"
    },
    {
      "citation": "Sengoku and Watanabe (2026), Absence of nontrivial local conserved quantities in a class of U(1)-symmetric spin-1 chains: related deficient symmetry-restricted families.",
      "url": "https://arxiv.org/abs/2608.17548",
      "doi": "10.48550/arXiv.2608.17548"
    }
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