{
  "abstract": "We establish a Harder-Narasimhan theory for torsion coherent $F$-gauges over a perfect field $k$ of positive characteristic and completely classify its stable objects. Our construction uses Ekedahl's derived equivalence with coherent complexes over the Raynaud ring, where the theory refines his half-integral type filtration on diagonal dominoes. At each finite rational slope $d/q$ in lowest terms, there is a unique stable diagonal domino up to Breuil-Kisin twist, constructed explicitly from the corresponding Christoffel word. The semistable category of this slope is equivalent to a product of $q$ copies of the zero-slope category. The classification of stable objects corrects Ekedahl's classification of weakly simple diagonal dominoes of type $\\frac{1}{2}$. The theory upgrades to a locally finite Bridgeland stability condition on $\\mathrm{Perf}_{\\mathrm{tor}}(k^{\\mathrm{Syn}})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27089",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuanning Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ehkzk1k6zzfx7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27089",
  "fulltext_url": null,
  "id": "ehkzk1k6zzfx7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27089",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214224007",
  "pdf_url": "https://arxiv.org/pdf/2609.27089",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ehkzk1k6zzfx7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27089",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27089"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Harder-Narasimhan filtration of torsion F-gauges",
  "title_text": "Harder-Narasimhan filtration of torsion F-gauges",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/ehkzk1k6zzfx7",
  "venue": "arXiv",
  "versions": []
}