{
  "abstract": "We introduce hammock coordinates to study the combinatorial structure of partial silting configurations in the bounded derived category of a derived-discrete algebra $Λ(r,n,m)$. By extracting exact integer inequalities from the Bobiński--Geiß--Skowroński Hom-hammock formula, we establish a closed-form criterion for pairwise partial silting both within any $\\mathcal Z$-component and across distinct components. Using this coordinate framework, we establish three primary results. First, we prove the universal upper bound $|S| \\le n+m$ on the cardinality of any partial silting configuration $S$ of $\\mathcal Z$-objects ---both globally via Bongartz completion in the silting-discrete setting, and combinatorially within a single component via a $Σ^r$-invariant staircase argument. Second, we prove that this bound is universally sharp by constructing an explicit L-shaped partial silting configuration of size $n+m$ for every $Λ(r,n,m)$, alongside specialized diagonal configurations. Third, we show that the configuration lattice carries a faithful action of the cyclic group $\\mathbb Z/g$ where $g = \\gcd(r+m, n-r)$. We conclude by showing a structural obstruction to local determination: pairwise partial silting of consecutive objects in the lattice ordering does not imply global partial silting, due to the strict additivity of a coordinate defect along chains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03204",
  "author_total": 1,
  "authors": [
    {
      "name": "Shantanu Sardar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61ghqqf6mf8jx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03204",
  "fulltext_url": null,
  "id": "61ghqqf6mf8jx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03204",
  "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.CT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03204",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61ghqqf6mf8jx.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03204",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03204"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hammock coordinates for silting subcategories of derived-discrete algebras",
  "title_text": "Hammock coordinates for silting subcategories of derived-discrete algebras",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/61ghqqf6mf8jx",
  "venue": "arXiv",
  "versions": []
}