[
  {
    "id": "ARR-2026-3NE8S0F70089P8PF-v1",
    "type": "article",
    "title": "The Reconstructed Theory Has One Mass: A Machine-Checked Volume-Uniform Transfer Gap for a Finite Ising Strip",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          7,
          28
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-3NE8S0F70089P8PF",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-3NE8S0F70089P8PF/versions/v1/",
    "note": "Archived manuscript; ARR-2026-3NE8S0F70089P8PF v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We give a finite-dimensional Osterwalder-Schrader reconstruction for an anisotropic Ising model on open rectangular strips and prove a spectral gap whose rate is uniform in the finite spatial extent. For temporal coupling beta, spatial coupling gamma, and parameters satisfying 0 < alpha < 1 and 2 tanh|beta| + 2 tanh|gamma| <= alpha, one number m > 0 works for every spatial length. Reflection positivity is proved directly for the Gibbs measure; the null space of the reflected form is identified with the kernel of an explicit boundary-collapse map; the OS quotient is linearly equivalent to the finite boundary-vector space; and the transfer operator forced by the site and bond forms is intertwined with a symmetrised transfer matrix.Dobrushin comparison supplies positive Perron data and a projected operator norm bounded by exp(-m) for every spatial length. Consequently, connected reconstructed correlations decay at the same common rate. Lean 4 checks thecomposition without assuming reflection positivity, Perron data, a vacuum, a gap, or clustering at the public endpoint. This replacement extends the point-slice, fixed-size v1 to finite strips with one rate uniform in spatial size. It does not construct an infinite-volume operator or Hamiltonian, provea unique particle excitation or relativistic mass shell, or claim a Yang-Mills mass gap."
  }
]