Pith Number

pith:OGNQBC4V

pith:2026:OGNQBC4VQ72KAYSDBBGFBOMQY2

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A Practical Introduction to Tensor Network Renormalization with TNRKit.jl

Adwait Naravane, Atsushi Ueda, Chenqi Meng, Victor Vanthilt

TNRKit extracts universal conformal data directly from fixed-point tensors in tensor network renormalization.

arxiv:2604.06922 v4 · 2026-04-08 · cond-mat.str-el · cond-mat.stat-mech · cs.MS · quant-ph

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

TNRKit enables the extraction of universal conformal data -- including scaling dimensions and the central charge -- directly from fixed-point tensors.

C2weakest 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.

C3one 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.

Receipt and verification

First computed	2026-06-09T02:07:26.108859Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

719b008b9587f4a06243084c50b990c68b11f8cb68c39aaa23c1bb5d14eb99ff

Aliases

arxiv: 2604.06922 · arxiv_version: 2604.06922v4 · doi: 10.48550/arxiv.2604.06922 · pith_short_12: OGNQBC4VQ72K · pith_short_16: OGNQBC4VQ72KAYSD · pith_short_8: OGNQBC4V

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OGNQBC4VQ72KAYSDBBGFBOMQY2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 719b008b9587f4a06243084c50b990c68b11f8cb68c39aaa23c1bb5d14eb99ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81de1fb03b064a28a26561d0c8265537114f4306be76dca279ec99a559817603",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cs.MS",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.str-el",
    "submitted_at": "2026-04-08T10:23:24Z",
    "title_canon_sha256": "1556e54b953be149c60ca71225ca9caca042f6f54f8cb75c9f4231e5bc69bb4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06922",
    "kind": "arxiv",
    "version": 4
  }
}