{"paper":{"title":"A Practical Introduction to Tensor Network Renormalization with TNRKit.jl","license":"http://creativecommons.org/licenses/by/4.0/","headline":"TNRKit extracts universal conformal data directly from fixed-point tensors in tensor network renormalization.","cross_cats":["cond-mat.stat-mech","cs.MS","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Adwait Naravane, Atsushi Ueda, Chenqi Meng, Victor Vanthilt","submitted_at":"2026-04-08T10:23:24Z","abstract_excerpt":"We present TNRKit, an open-source Julia package for Tensor Network Renormalization (TNR) of two- and three-dimensional classical statistical models and Euclidean lattice field theories. Built on top of TensorKit, it provides a symmetry-aware framework for constructing tensor-network representations of partition functions and coarse-graining them using methods such as TRG, HOTRG, and LoopTNR. Beyond thermodynamic quantities, the package enables the extraction of universal conformal data -- including scaling dimensions and the central charge -- directly from fixed-point tensors. TNRKit is design"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"TNRKit enables the extraction of universal conformal data -- including scaling dimensions and the central charge -- directly from fixed-point tensors.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The implemented coarse-graining routines produce fixed-point tensors whose eigenvalues and eigenvectors faithfully encode the universal data of the underlying model without significant truncation artifacts or symmetry-breaking errors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"TNRKit is a symmetry-aware Julia package that implements TRG, HOTRG, and LoopTNR to coarse-grain tensor networks and extract conformal data such as scaling dimensions and central charge from fixed-point tensors.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"TNRKit extracts universal conformal data directly from fixed-point tensors in tensor network renormalization.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f3328a2368ad42b2734551f7ddb026bef693c3935b5ef973bd2721895ac19c39"},"source":{"id":"2604.06922","kind":"arxiv","version":4},"verdict":{"id":"eec83bf5-56ac-4a1f-bfa8-aee8725356dc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T17:57:52.637351Z","strongest_claim":"TNRKit enables the extraction of universal conformal data -- including scaling dimensions and the central charge -- directly from fixed-point tensors.","one_line_summary":"TNRKit is a symmetry-aware Julia package that implements TRG, HOTRG, and LoopTNR to coarse-grain tensor networks and extract conformal data such as scaling dimensions and central charge from fixed-point tensors.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The implemented coarse-graining routines produce fixed-point tensors whose eigenvalues and eigenvectors faithfully encode the universal data of the underlying model without significant truncation artifacts or symmetry-breaking errors.","pith_extraction_headline":"TNRKit extracts universal conformal data directly from fixed-point tensors in tensor network renormalization."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.06922/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}