[
  {
    "id": "ARR-2026-0BQ1X4SGFJ8AJ8N1-v2",
    "type": "article",
    "title": "Positive circuit obstructions and rigidity for lattice-fiber log-concavity",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          27
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-0BQ1X4SGFJ8AJ8N1",
    "version": "v2",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-0BQ1X4SGFJ8AJ8N1/versions/v2/",
    "note": "Research preprint; ARR-2026-0BQ1X4SGFJ8AJ8N1 v2. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We characterize the full-row-rank integer matrices whose lattice-point counts satisfy midpoint log-concavity in every fixed integer coordinate box. Under the promise that all three integer fibers are nonempty, the property holds exactly for equimodular matrices, whose nonzero maximal minors have one common magnitude. The same classification holds coefficientwise and at positive external fields. Necessity has an explicit certificate: a primitive minimal kernel circuit with a coefficient of magnitude at least two gives counts (1,1,2) in one box supported on at most r+1 coordinates. Its defect is one negative monomial, so the same triple violates the inequality at every positive field. If empty fibers are allowed for arbitrary ambient integral right-hand sides, the common minor magnitude must additionally be odd. Classical circuit and lattice-normalization results supply the structural tools, while sufficiency uses Leake--Mohammadi Yekta’s coefficientwise inequality. We retain equality by integral translations via squarefreeness of complete lattice enumerators, and a test using 6n linear optimizations. The rational-box boundary and the distinction from global Jensen remain explicit. Exact finite controls have a byte-preserving reproduction supplement."
  }
]