[
  {
    "id": "ARR-2026-0BQ1X4SGFJ8AJ8N1-v1",
    "type": "article",
    "title": "Rigidity and strongly polynomial equality tests for unimodular fiber counts",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          27
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-0BQ1X4SGFJ8AJ8N1",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-0BQ1X4SGFJ8AJ8N1/versions/v1/",
    "note": "Research preprint; ARR-2026-0BQ1X4SGFJ8AJ8N1 v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "Leake and Mohammadi Yekta proved coefficientwise midpoint log-concavity for lattice-point enumerators of unimodular box fibers. We characterize its equality cases. For three nonempty fibers in one integer coordinate box, equality at one positive external field is equivalent to symmetric integral translation of the three real fiber polytopes. Equality is independent of the field, and unweighted equality forces all three counts to coincide. The proof uses a squarefreeness lemma for the complete lattice-point enumerator of any lattice polytope. A product of k such enumerators can be the kth power of another only when their polytopes are integral translates with shifts summing to zero. Coordinate extrema yield an equality test using six linear optimizations per coordinate and no lattice-point enumeration. Basis normalization and Tardos's algorithm give a strongly polynomial number of arithmetic operations under the integer-box promise, with input-dependent bit costs. We explain the rational-box boundary, strictness consequences and a weighted realization obstruction. No global Jensen inequality is established."
  }
]