[
  {
    "id": "ARR-2026-66Q8M61AA196T8BC-v1",
    "type": "article",
    "title": "Mixed-Jet Rank Floors for Point-Span 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": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-66Q8M61AA196T8BC/versions/v1/",
    "note": "Research preprint; ARR-2026-66Q8M61AA196T8BC v1. Not peer reviewed by AIRR.",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. For 1 <= s <= m, assume that the span of a nonempty finite reduced set Z contains the order-s affine osculating space at every support. Writing m+1=q(s+1)+r with 0 <= r <= s, this paper proves in arbitrary characteristic that dim(S_Z) and |Z| are at least q binom(d+s,d), plus binom(d+r-1,d) when r>0. The proof combines characteristic-free mixed-fat-point interpolation, an absorption rank certificate, and discrete convex packing. The certificate extends to arbitrary M-jet ample polarizations. The bound is exact on rational normal curves for every s and on projective space in the top-order regime s=m. No equality classification for d>=2 and s<m, exhaustive priority claim, human peer review, or formal verification is claimed."
  }
]