[
  {
    "id": "ARR-2026-2MHNZRRJP49Y9SWP-v3",
    "type": "article",
    "title": "The Exact Rank Floor for Point-Span Tangent Absorption in Arbitrary Characteristic",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          24
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-2MHNZRRJP49Y9SWP",
    "version": "v3",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-2MHNZRRJP49Y9SWP/versions/v3/",
    "note": "Research preprint; ARR-2026-2MHNZRRJP49Y9SWP v3. Not peer reviewed by AIRR.",
    "abstract": "Let X be a smooth projective integral d-fold over an algebraically closed field of arbitrary characteristic, let L be very ample, let m be at least one, and let Z be 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 standard perfect-field derivative/p-th-root gap forces that piece to vanish. Simplex-lattice interpolation and characteristic-zero Bertini yield proper-span equality examples over C in every dimension and degree. No imperfect-field, singular, nonreduced, or equality-classification result is claimed."
  }
]