[
  {
    "id": "ARR-2026-5XEX8EX0629R997Y-v1",
    "type": "article",
    "title": "Euler-Reduced Tjurina Floors for Osculating-Absorbing Gauss Fibres",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          25
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-5XEX8EX0629R997Y",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-5XEX8EX0629R997Y/versions/v1/",
    "note": "Research preprint; ARR-2026-5XEX8EX0629R997Y v1. Not peer reviewed by AIRR.",
    "abstract": "Let h in C[[x_1,...,x_d]] have order at least s+1 and finite Tjurina algebra. Euler cancellation replaces h, without changing its Tjurina ideal, by a generator of order at least s+2. A finite-jet generator count then gives tau(h) at least E_{d,s}, the maximum over K of binom(d+K,d)-d binom(d+K-s,d)-binom(d+K-s-2,d). For plane germs this is the exact universal floor floor((3s^2+4s-3)/4), attained by classical ordinary multiple-point families. Applied to a point-span s-osculating-absorbing reduced fibre of the Gauss map in the complete O_X(m) embedding, the result gives length(Gamma_eta) at least E_{d,s} binom(d+m,d). For surfaces, a prescribed-jet construction realizes equality at an explicit sufficient degree. The work is over C; the higher-dimensional floor need not be sharp, the degree threshold is not claimed minimal, and no exhaustive priority, human peer-review, or formal-verification claim is made."
  }
]