[
  {
    "id": "ARR-2026-3FHSR0Q6W49X38F6-v1",
    "type": "article",
    "title": "Endpoint Parity Loss in a Bessel Wronskian: an Exact Obstruction to Kernel-and-Anchor Proofs of Global Ratio Monotonicity",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          4
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3FHSR0Q6W49X38F6",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-3FHSR0Q6W49X38F6/versions/v1/",
    "note": "Archived manuscript; ARR-2026-3FHSR0Q6W49X38F6 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "For beta > 0 let I_m = I_m(beta) denote the modified Bessel functionof the first kind and define  a_m = I_m^2 ((m-1) I_(m-1)^2 + (m+1) I_(m+1)^2),  b_m = m I_m^4,with sine series F_A(t) = sum_(m>=1) a_m sin(mt) andF_B(t) = sum_(m>=1) b_m sin(mt). The associated Wronskian is negativeexactly when F_A/F_B is decreasing. We isolate what can and cannot beproved from two natural inputs: the Neumann convolution kernelI_0(2 beta sin(phi/2)) and the small-coupling anchor whose normalizedlimit is 4 sin^3(t).First, the convolution does prove F_B(t) > 0 for 0 < t < pi. Second,the endpoint is governed by two alternating quantities, c_3 and B_pi,through an exact cubic law. We prove B_pi > 0, derive integralrepresentations, and establish that the cancellation lost by replacingthe alternating quantities with positive-term majorants has exponentialrate 8 - 4 sqrt(2). Finally, we prove a smooth one-parameter perturbationtheorem: one may keep F_B and its kernel unchanged, preserve positivityand strict coefficient-ratio ordering, and preserve every jet at beta = 0,while choosing either sign of the endpoint cubic coefficient.Consequently those structural data, even taken together, do not implyglobal Wronskian negativity. This is a no-go theorem for a proofarchitecture, not a counterexample to the original Bessel conjecture.A short high-precision kill-test accompanies the paper; nocomputer-assisted inequality is used in the proofs."
  }
]