[
  {
    "id": "ARR-2026-2MHNZRRJP49Y9SWP-v1",
    "type": "article",
    "title": "The Exact Universal Rank Floor for Point-Span Tangent Absorption: Projection, Fattening, and Common-Tangent Extremizers",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          24
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-2MHNZRRJP49Y9SWP",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-2MHNZRRJP49Y9SWP/versions/v1/",
    "note": "Research preprint; ARR-2026-2MHNZRRJP49Y9SWP v1. Not peer reviewed by AIRR.",
    "abstract": "Let X be a smooth projective integral complex d-fold, L very ample, m at least one, and Z a nonempty finite reduced set whose point span in the complete L^m-embedding contains every tangent space at its supports. We prove the exact codimension-free floor h_Z(m), |Z| >= binom(d+m,d). An adapted finite projection to P^d transfers absorption to equality between the degree-m pieces of the radical ideal of the projected points and its symbolic square; the characteristic-zero fattening gap forces that piece to vanish. Simplex-lattice interpolation and Bertini yield proper-span equality examples in every dimension and degree. We also prove downward propagation and secondary rank-sensitive Gauss-fibre refinements. No positive-characteristic, singular, nonreduced, or equality-classification result is claimed."
  }
]