[
  {
    "id": "ARR-2026-3CEWH763KG84B8TM-v1",
    "type": "article",
    "title": "Global Ratio Monotonicity for a Killed von Mises Bridge",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          7,
          28
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3CEWH763KG84B8TM",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-3CEWH763KG84B8TM/versions/v1/",
    "note": "Archived manuscript; ARR-2026-3CEWH763KG84B8TM v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "For beta > 0 let I_m = I_m(beta) denote modified Bessel functions ofthe first kind, and set  a_m = I_m^2 [(m-1) I_(m-1)^2 + (m+1) I_(m+1)^2],  b_m = m I_m^4,  F_A(t) = sum_(m>=1) a_m sin(mt),  F_B(t) = sum_(m>=1) b_m sin(mt),  E(t) = F_A(t)/(2 F_B(t)).The global ratio-monotonicity problem for the surface expansion of atwo-dimensional SU(2) lattice gauge observable is: (i) F_B > 0 on(0,pi), and (ii) E' < 0 on (0,pi), for every beta > 0. Bothstatements are proved. Positivity of F_B has two exact proofs. Ratiomonotonicity is reduced to exact algebraic identities andoutward-rounded interval certificates: small and compact beta arehandled by pair identities and interval Taylor models;20 <= beta <= 1000/9 by a direct Wronskian cover; andbeta >= 1000/9 has three certified moving-edge lambda lanes. Theremaining lambda >= 3 lane is closed by the exact identityE'/(-sin(t/2)/2) = Q + X_full, where Q > 19/20, an exactmain--mirror--rest decomposition, and a division-free covariancecertificate proving X_main > -1/20 on two adjacent rectangles thatcover the full angular interval. The exact near and far relay marginsare positive. All load-bearing production and independent replaytranscripts are checked for exact rational coverage, dependencyhashes, strict outward-rounded decision endpoints, and byte equality.The structural core is exact: E is, as an algebraic identity, the meanof cos(psi) under the midpoint law of a four-step killed von Misesbridge; the generating kernels reduce, via the Neumann additiontheorem, to two-dimensional integrals of a single Bessel functionwhose saddle deficit is an exact sum of two squares; and exact saddlecancellations yield the coefficients of the verified closedsecond-order law  E = cos(t/2)(1 - c(t)/beta) + O(beta^-2),  c(t) = (4 cos^2(t/4) - 1)/(2 cos(t/4) cos(t/2)).Three certified negative results (interval arithmetic, twoimplementations, nested enclosures) kill every monotone full-pathcoupling, with an exact mechanism at threshold beta |cos t| = 3/2. Atthe pi endpoint we also give exact identities for the cubiccoefficient c_3 (telescoped alternating form, integral form, parity)together with its verified prefactor law. Every claim is labelledexact / certified / verified; the machine-checked lemmas are Lean4/Mathlib, machine-checked modulo classical Bessel inputs carried asnamed hypotheses."
  }
]