[
  {
    "id": "ARR-2026-3B7MWNSJS18TYAA4-v1",
    "type": "article",
    "title": "Machine-Checked Finite-Edge SU(2) Crossing Ward Identity: Pauli Generator Transfer and Single-Trace Closure",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          2
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3B7MWNSJS18TYAA4",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-3B7MWNSJS18TYAA4/versions/v1/",
    "note": "Archived manuscript; ARR-2026-3B7MWNSJS18TYAA4 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We formalize a finite-dimensional crossing Ward identity for fundamental SU(2) Wilson words. On every finite edge space SU(2)^E, two distinct coordinates are inserted into a concrete normalized trace word. Lean proves entrywise that right multiplication by each of three explicit SU(2) curves produces the normalized Pauli generators i sigma_a/2, differentiates the trace word once at each selected coordinate, and identifies the Pauli-summed mixed derivative with the rank-two Fierz contraction. Two applications of Haar integration by parts transfer the corresponding mixed generators from a density to the Wilson word. The resulting integral closes exactly on the direct and reverse single-trace resolutions, with coefficients -1/4 and -1/2 in the chosen normalization. The producer contains 19 public declarations in 487 physical lines; all 13 new theorems depend only on propext, Classical.choice, and Quot.sound, with no local sorry, admit, or axiom. This is not a full Makeenko--Migdal area equation: the remaining physical input is a weak four-face identity against crossing-certified extended-gauge-invariant observables. In the program's heat time, generated by the Pauli Laplacian, its coefficient is kappa = 2."
  }
]