Pith Number

pith:4PGVQEZS

pith:2021:4PGVQEZSAWS7VOUXSWDH3NI6LH

not attested not anchored not stored refs pending

Low moments of the four-loop splitting functions in QCD

Amsterdam), A. Vogt (Liverpool U., B. Ruijl (Zurich, Dept. Math), ETH), Inst. Theor. Phys. II), J.A. M. Vermaseren (NIKHEF, S. Moch (Hamburg U., T. Ueda (Seikei U.)

arxiv:2111.15561 v1 · 2021-11-30 · hep-ph

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4PGVQEZSAWS7VOUXSWDH3NI6LH}

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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

4 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

Properties and implications of the four-loop non-singlet splitting functions in QCD

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	2026-07-05T03:45:55.145738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3cd58133205a5faba9795867db51e59d912fd42250c1e7adbb9f0ae1981ec81

Aliases

arxiv: 2111.15561 · arxiv_version: 2111.15561v1 · doi: 10.48550/arxiv.2111.15561 · pith_short_12: 4PGVQEZSAWS7 · pith_short_16: 4PGVQEZSAWS7VOUX · pith_short_8: 4PGVQEZS

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/4PGVQEZSAWS7VOUXSWDH3NI6LH \
  | 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: e3cd58133205a5faba9795867db51e59d912fd42250c1e7adbb9f0ae1981ec81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fdd4b253baee951c8dcb343c98f290b62b50d7a676425d35656b4f9f44bb858",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2021-11-30T16:54:04Z",
    "title_canon_sha256": "6591c228e107aa4c88f425f8b0b3b2109e057748276266629c58f423cb202752"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.15561",
    "kind": "arxiv",
    "version": 1
  }
}