{
  "abstract": "We study prescribed holomorphic lattices for regular-singular connections and residual factors of quantum $F$-bundles. For an arbitrary ordered monodromy spectrum, we classify the fully framed local groupoid: each residue fibre is a discrete affine space of dimension $r(r-1)$, with a unique normal form and trivial stabilisers. We then analyse elementary changes of lattice. A strictly positive integral residue difference obstructs the oriented wall; otherwise, in arbitrary rank, the extending normal-form arcs form an affine torsor of relative dimension $r(r-1)$, and specialisation to the shifted residue slice is polynomial and triangular by root height. Adjacent walls exhibit the composite-root correction dictated by the type-$A$ root-subgroup relations, while an example over the dual numbers detects a nilpotent saturation defect. For one-branch $F$-bundles, the scalar branch is recovered from the residual trace, and scalar residualisation yields a symmetric monoidal equivalence with zero-branch $F$-bundles. This construction yields residual atoms, functorial Jordan strata, and a residual chemical formula compatible with blow-ups and projective bundles. In the $A$-model, residualisation removes the unit direction; the rationally marked large-radius residual germ recovers the divisor cubic and distinguishes the marked residual germs of the Pfaffian and Grassmannian Calabi--Yau threefolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27723",
  "author_total": 1,
  "authors": [
    {
      "name": "Mauricio Corrêa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/023556m41nrbw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27723",
  "fulltext_url": null,
  "id": "023556m41nrbw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27723",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223123375",
  "pdf_url": "https://arxiv.org/pdf/2610.27723",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/023556m41nrbw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27723",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27723"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lattice Moduli and Residual Atoms",
  "title_text": "Lattice Moduli and Residual Atoms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/023556m41nrbw",
  "venue": "arXiv",
  "versions": []
}