[
  {
    "id": "ARR-2026-5BJDY6QKSH9QBTQS-v1",
    "type": "article",
    "title": "Modular Recovery from Split Inclusions: A B-minimal Bridge from QFT Collar Geometry to Approximate State Reconstruction",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          1,
          11
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-5BJDY6QKSH9QBTQS",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-5BJDY6QKSH9QBTQS/versions/v1/",
    "note": "Archived manuscript; ARR-2026-5BJDY6QKSH9QBTQS v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "In algebraic quantum field theory (AQFT), local algebras are typically Type III factors, so density matrices and von Neumann entropies are unavailable for bounded regions. We formulate a B-minimal continuum analog of the lattice \"collar => Markovness => recovery\" mechanism by combining: (i) the split property as the mathematical replacement of a buffer (collar), (ii) Araki relative entropy to define a split-regularized conditional mutual information I^N(A:C|B) relative to fixed Type I interpolating data N, and (iii) modular/twirled Petz recovery as an explicit candidate recovery channel. Assuming an FR-type recoverability inequality in the fixed-split setting, we obtain quantitative recovery bounds in a fidelity-based error metric (purified distance). We conclude with a conditional holographic remark. v2 corrects the fidelity-convention factor in the assumed FR-type inequality: with the squared (Bures/Uhlmann-squared) convention used throughout, the importable finite-dimensional motivation gives -log F <= I, not -log F <= I/2; v1's half-form is strictly stronger than its motivation and is refuted as a finite-dimensional anchor on 40/40 random tripartite states (the corrected form holds on 40/40) -- the same factor-2 correction applied in 2512.0101 v2 and 2601.0020 v2. The recovery theorem's constant changes by sqrt(2); the exponent is unaffected. v2 further adds series positioning, a compatibility remark with the split-regularized CMI of 2601.0020, a concrete demonstration that I^N can be negative for unfavorable split data -- nonnegativity of I^N is part of the good-split-data regime, not automatic -- and a finite-dimensional verification suite for every checkable ingredient of the dictionary."
  }
]