[
  {
    "id": "ARR-2026-7D2BBEC8MJ8BM80S-v1",
    "type": "article",
    "title": "Cellulation-Independent Boundary Gauge Averaging and Sharp Class-Sector Gaps in Two-Dimensional Yang--Mills",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          15
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-7D2BBEC8MJ8BM80S",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-7D2BBEC8MJ8BM80S/versions/v1/",
    "note": "Research preprint; ARR-2026-7D2BBEC8MJ8BM80S v1. Not peer reviewed by AIRR.",
    "abstract": "Let G be a compact connected Lie group with a bi-invariant metric. For the two-dimensional heat-kernel Yang--Mills model, this paper gives an explicit finite chain from a boundary-conditioned edge integral on an arbitrary regular annular cellulation to the gauge-invariant class-function transfer kernel. Conditional Haar coordinates make the boundary constraints and boundary-edge subdivision precise. Edge and face subdivision invariance, an explicit PL radial-cut construction, and a primal-tree/dual-cotree disk-elimination schedule yield a cellulation-independent orbital heat-kernel integral. Peter--Weyl theory then diagonalizes the transfer operator with multipliers exp(-t c_lambda). The exact mean-zero norm is exp(-t c_*(G)), the gap of I-T_t is 1-exp(-t c_*(G)), and the equality sector consists of all irreducible characters with minimum positive Casimir. In the stated SU(2) normalization the sharp exponent is 3/4, while the induced SO(3) quotient removes the fundamental channel and raises it to 2. The work assembles and audits classical two-dimensional Yang--Mills ingredients; it does not claim a new character solution, four-dimensional mass gap, continuum reconstruction, or clustering for arbitrary bulk observables."
  }
]