Beyond Gaussianity: Extending the Clustering-Recovery Bridge
Earlier deposit preserved without the current AIRR screening. Not peer reviewed. Screening record
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.
Preview PDF on this page v1
Uses your browser's PDF viewer. Open the PDF directly if a preview is unavailable.
Cite this paper
Lluis Eriksson (2025). Beyond Gaussianity: Extending the Clustering-Recovery Bridge. AIRR.SCIENCE, ARR-2025-6NR077ZRZ19NJ8RG, v1. https://airr.science/papers/ARR-2025-6NR077ZRZ19NJ8RG/versions/v1/ Archived manuscript; ARR-2025-6NR077ZRZ19NJ8RG v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.
Use this version link to cite the manuscript you read. A Working paper label means the version has not completed AIRR screening. AIRR screening is not journal peer review. Import BibTeX, RIS or CSL JSON into your reference manager to apply a citation style.
Version history
The paper 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; AIRR preserves the displayed values and uses the normalized offset only for deterministic ordering.
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. AIRR verification and screening are not peer review.
AI assistance statement
Historical import from ai.vixra, an AI-assisted e-print archive. AIRR 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.
Model assessments and review context
No supported exact-version 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. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Author-authorized historical import. AIRR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification.