[
  {
    "id": "ARR-2026-7RASMSMHWW8PM9S8-v1",
    "type": "article",
    "title": "A Non-Gaussian Clustering-Recovery Bridge via Conditional Mutual Information: Interacting Gibbs States, Explicit Petz Benchmarks, and a Conditional Link to Entanglement Wedge Reconstruction",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          1,
          11
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-7RASMSMHWW8PM9S8",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-7RASMSMHWW8PM9S8/versions/v1/",
    "note": "Archived manuscript; ARR-2026-7RASMSMHWW8PM9S8 v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We present a quantitative clustering-recovery bridge for interacting quantum many-body systems that is intrinsically non-Gaussian, organized around conditional mutual information (CMI). For a geometric tripartition A-B-C in which B is a collar of width w separating A from C, an exponential geometric Markov bound I(A:C|B) <= K e^(-alpha w) implies exponentially accurate recovery of rho_ABC from rho_AB in the theorem-facing metric -log F, by combining the Fawzi-Renner inequality with an elementary conversion to fidelity error bounds. We obtain a proved interacting lane (shielded small-region geometry, arbitrary temperature) by invoking recent local Markovness results for finite-range lattice Gibbs states. Numerically, we benchmark the mechanism in the transverse-field Ising chain with longitudinal field, comparing integrable (hz = 0) and non-integrable (hz = 0.5) regimes, and evaluate the explicit Petz recovery map with a censored log-plotting and fit protocol. v2 corrects the Fawzi-Renner factor under the squared-fidelity convention used throughout (-log F <= I, not I/2; fourth occurrence of this correction in the series), with a substantive empirical consequence: v1's headline \"mild overshoot\" of Petz over the FR scale (r of about 1.23-1.26 in the non-integrable, low-temperature, minimal-collar regime, including rotated and twirled controls) was measured against the incorrect half scale; against the corrected scale the overshoot disappears entirely (r of about 0.62), and the v1 conclusion of \"a genuine gap between explicit Petz-type constructions and the existential optimal-recovery scale\" is withdrawn. The corrected conclusion is stronger: explicit Petz satisfies the FR scale throughout the dataset, with at least about 40 percent margin even at the hardest point. A fully regenerable verification suite reproduces the pipeline from scratch. Finally, we state a conditional application to entanglement wedge reconstruction, separating proved information-theoretic content from bulk-boundary interface assumptions."
  }
]