[
  {
    "id": "ARR-2026-66Q8M61AA196T8BC-v2",
    "type": "article",
    "title": "Exact Floors and Proper-Span Extremizers for Higher Osculating Absorption",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          24
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-66Q8M61AA196T8BC",
    "version": "v2",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-66Q8M61AA196T8BC/versions/v2/",
    "note": "Research preprint; ARR-2026-66Q8M61AA196T8BC v2. Not peer reviewed by AIRR.",
    "abstract": "Let X be a smooth projective integral d-fold over an algebraically closed field, let H be very ample, and use the complete embedding defined by H^m. Fix 1 <= s <= m and suppose that the span of a nonempty finite reduced set Z contains the order-s affine osculating space at every support. We prove the exact characteristic-free floor dim(S_Z), |Z| >= binom(d+m,d), by reduction to exact tangent absorption. For every d, m, s and every characteristic, we construct a smooth integral hypersurface with a proper-span equality set whose normal coordinate vanishes to order s+1 at every support. If r_1(Z) is the degree-one evaluation rank and m >= 2s+1, we also prove the rank-sensitive term binom(d+s,d) r_1(Z); rational normal curves show the threshold is necessary for that uniform formula. The earlier mixed-jet certificate is retained for jet-ample polarizations but identified as numerically subordinate for tensor powers. No equality classification, minimal hypersurface degree, exhaustive priority claim, human peer review, or formal verification is claimed."
  }
]