Pith Number

pith:3JRUJ7HN

pith:2023:3JRUJ7HNFIOOIJ7KD7YRZVFKFW

not attested not anchored not stored refs pending

Renormalization of twist-two operators in covariant gauge to three loops in QCD

Andreas von Manteuffel, Thomas Gehrmann, Tong-Zhi Yang

arxiv:2302.00022 v1 · 2023-01-31 · hep-ph · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3JRUJ7HNFIOOIJ7KD7YRZVFKFW}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

3 papers in Pith

Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part

The four-loop non-singlet splitting functions in QCD

Receipt and verification

First computed	2026-07-05T09:41:26.946579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da6344fced2a1ce427ea1ff11cd4aa2d9cbd0ebda8bf689ccb4c6a53abff324a

Aliases

arxiv: 2302.00022 · arxiv_version: 2302.00022v1 · doi: 10.48550/arxiv.2302.00022 · pith_short_12: 3JRUJ7HNFIOO · pith_short_16: 3JRUJ7HNFIOOIJ7K · pith_short_8: 3JRUJ7HN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3JRUJ7HNFIOOIJ7KD7YRZVFKFW \
  | 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: da6344fced2a1ce427ea1ff11cd4aa2d9cbd0ebda8bf689ccb4c6a53abff324a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a37ddeddba17a10200f4dfc868e4c2ee3744a09af1d257f59a6f0aba928f4a73",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2023-01-31T19:00:12Z",
    "title_canon_sha256": "acaa4a7a33f9b753d0201a9deede0815b749450128a84aa25d8f26a58fd4c9ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2302.00022",
    "kind": "arxiv",
    "version": 1
  }
}