[
  {
    "id": "ARR-2026-72G1SSCNNG8YDVC2-v1",
    "type": "article",
    "title": "A Weighted Turan-Type Monotonicity Lemma for Modified Bessel Functions via the Calibrated Amos Bound, with an Application to the Ordering of a Surface Expansion in Two-Dimensional Lattice Gauge Theory",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          7,
          9
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-72G1SSCNNG8YDVC2",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-72G1SSCNNG8YDVC2/versions/v1/",
    "note": "Archived manuscript; ARR-2026-72G1SSCNNG8YDVC2 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "For x>0 and real m>=1 define phi_m(x) = [(m-1) I_{m-1}(x)^2 + (m+1) I_{m+1}(x)^2] / (m I_m(x)^2), with I_mu the modified Bessel function of the first kind. We prove phi_m(x) < phi_{m+1}(x) for every x>0 and everyreal m>=1 - a weighted Turan-type monotonicity statement we have not found in the literature, although every ingredient of the proof is classical. The proof is fully elementary: eliminating the neighbouring ratios by thethree-term recurrence, the difference factorizes exactly as (S-3c)(P-(2m+1)c) + (2m+1)c^2, with u = I_{m+1}/I_m, c = 1/x, S = u+1/u, P = 1/u-u; the second factor is positive by the calibrated Amos bound (it is precisely the unit-step inequality of the companion note), the first because the same bound forces u < x/(2m+1) <= x/3. As an application we obtain thestrict determinant ordering c_mn < 0 (m"
  }
]