[
  {
    "id": "ARR-2026-2MZWECWVEN97ARVQ-v1",
    "type": "article",
    "title": "Fat Gauss Fibres and Tjurina–Milnor Defects Forced by Osculating Absorption",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          25
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-2MZWECWVEN97ARVQ",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-2MZWECWVEN97ARVQ/versions/v1/",
    "note": "Research preprint; ARR-2026-2MZWECWVEN97ARVQ v1. Not peer reviewed by AIRR.",
    "abstract": "Let X be a smooth non-linear complex hypersurface and let Gamma_eta be the scheme-theoretic fibre of its Gauss normalization over a tangent hyperplane. The completed local fibre algebra is the Tjurina algebra of the tangent-section germ, while the classical dual multiplicity is the sum of its Milnor numbers; hence their difference is the total Tjurina–Milnor defect. Under point-span order-s osculating absorption in the complete O_X(m) embedding, the fibre contains the order-s fat point at every reduced support and has length at least binom(d+s-1,d) binom(d+m,d). When d(s-1)>s+1, prescribed jets realize every integral defect from 0 through the extremal support size while keeping all Milnor numbers fixed. The degree threshold is sufficient, not minimal; no positive-characteristic extension, exhaustive priority claim, human peer review, or formal verification is claimed."
  }
]