Research paperHistorical importARR-2025-6NR077ZRZ19NJ8RG · v1 · 2025-12-31

Beyond Gaussianity: Extending the Clustering-Recovery Bridge

Lluis Eriksson

Abstract

We formulate a non-Gaussian, finite-volume and uniform-in-Lambda version of the Clustering-Recovery bridge for interacting lattice systems. We introduce an explicit collar geometry, a CMI formulation via Fawzi-Renner, and an operational (Heisenberg-picture) quasi-locality strengthening for the recovery map. Version 2 corrects one identity: v1's "CMI as relative entropy" equation equated I(A:C|B) with the relative entropy to the normalized Markov-product state; the exact identity holds for the unnormalized product M = exp(log rho_AB + log rho_BC - log rho_B), and the normalized version underestimates the CMI by -log Z >= 0 (Z <= 1 by Lieb's triple-matrix inequality). We also fix the Fawzi-Renner factor: with the squared-fidelity convention used throughout, the bound is I(A:C|B) >= -log F (not -2 log F). All numerical claims of v1 (Petz slope table; prefactor-slope trade-off; crossover w*=3) have been independently reproduced from scratch by a NumPy-only verification script that ships with this paper.

Download mirrored PDFDownload release assetsBrowse plain sources
Original depositai.vixra first-submission history · source omits timezone
Historical mirrorv2Author-authorized ARR bulk release · SHA-256 recorded
Mirrored PDF downloadsNot measuredBulk historical-release assets are not yet included in ARR's per-record download snapshot.
Page viewsNot measuredPage views are not measured until ARR connects a privacy-reviewed, no-cookie analytics source.
Definitions and rankings →
Not yet rated

Verification record

Frontier-model screening
Not assessed
Source integrity
Pass
Bibliographic integrity
Not assessed
Reproducibility
Not assessed
Lean 4
Not assessed

Recorded under ARR-HISTORICAL-IMPORT-1.0. ARR verification and screening are not peer review.

Version history

The ARR identifier remains stable. Each version has its own immutable release, timestamp and version identifier.

  • v1 · source snapshot available · viewing

Original ai.vixra version history

Dates below are the source submission timestamps. ai.vixra omits a timezone; ARR preserves the displayed values and uses the normalized offset only for deterministic ordering.

  • v2 · original ai.vixra file
  • v1 · original ai.vixra file

AI assistance statement

Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents.

Frontier-model screening

Status: not_assessed. Any listed reports correspond to this exact version under ARR-SCREEN-1.0; no absent assessment is represented as a pass.

    Longitudinal frontier-model record

    Independent model assessments

    Read the scale and limits
    Not yet rated

    No eligible independent ARR-ASSESS-1.0 report is published for this exact version. Missing evidence is not scored as zero.

    No model reports are published for this version.

    A model assessment is not peer review or a correctness certificate. ARR preserves disagreement, exact-version provenance and later reassessments.

    Editorial disclosure

    Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification.