[
  {
    "id": "ARR-2026-51CS1EZ4K28W7TB3-v1",
    "type": "article",
    "title": "From Dobrushin Comparison to a Quasi-Local C*-State: A Lean-Checked Construction for the Two-Dimensional Ising Model",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          5
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-51CS1EZ4K28W7TB3",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-51CS1EZ4K28W7TB3/versions/v1/",
    "note": "Archived manuscript; ARR-2026-51CS1EZ4K28W7TB3 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We present a Lean 4 formalization of a thermodynamic-limit construction for the anisotropic nearest-neighbour Ising model on the two-dimensional integer lattice. A telescoping comparison argument and the classical Dobrushin resolvent produce a volume-uniform expectation bound. Exact restriction and reindexing maps between finite Gibbs measures yield convergence of the complete free-boundary sequence, independence of auxiliary envelopes and cofinal samplings, stability under receding boundary perturbations, and equality of free and periodic limits.Finite-support cylinder presentations are quotiented by equality of their represented functions on the full spin space. The resulting local algebra carries a genuine lattice-translation action, and the limiting functional is positive, normalized, real-linear, and invariant under every integer translation. We equip this algebra with its intrinsic uniform norm, construct its complex star-algebra representation, take the corresponding commutative C*-closure, and extend the limiting functional to a positive complex-linear functional of norm one. We also formalize normalized Gibbs conditional kernels for arbitrary finite conditioning sets and prove positivity, exterior locality, idempotence, and the exact finite-volume Gibbs tower identity.All results remain within the classical anisotropic Dobrushin region. The infinite-volume DLR fixed-point equation for the completed state is not claimed."
  }
]