[
  {
    "id": "ARR-2026-5V5K6T6DQT9J8SY6-v1",
    "type": "article",
    "title": "Machine-Checked Haar and Differential Descent at an SU(2) Crossing: A Four-Edge Compensated-Flow Ward Identity",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          2
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-5V5K6T6DQT9J8SY6",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-5V5K6T6DQT9J8SY6/versions/v1/",
    "note": "Archived manuscript; ARR-2026-5V5K6T6DQT9J8SY6 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We machine-check the exact measure and differential bridge between thefour-edge SU(2) crossing chart and the two effective group coordinates used bya finite-dimensional Ward identity. The quotientr(a)=(a2 a4^-1,a1 a3^-1) pushes normalized four-fold Haar measure exactly tonormalized two-fold Haar measure. Two gauge-compensated flows on the originalfour edges intertwine with independent right multiplication of the quotientcoordinates, so first and mixed derivatives of the crossing Wilson worddescend without choosing a gauge. The three Pauli directions are verifiedindividually, their mixed generators close into direct and reverseresolutions, and the two-coordinate Ward theorem lifts to a literal four-edgeintegral with coefficients -1/4 and -1/2. This compensated operator is notidentified with the ordinary-edge mixed operator of Driver-Hall-Kemp: thepaper writes both operators and their distinct reverse resolutions and markstheir comparison as open. The Lean producer has 26 public declarations and 16audited theorems. No weak four-face heat-kernel identity, area derivative, orfull Makeenko--Migdal equation is claimed."
  }
]