Pith Number

pith:3XIXR6EM

pith:2004:3XIXR6EMGUF64TVPI35O4MD4H3

not attested not anchored not stored refs pending

The Four-Loop QCD Beta-Function and Anomalous Dimensions

M. Czakon

arxiv:hep-ph/0411261 v2 · 2004-11-19 · hep-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3XIXR6EMGUF64TVPI35O4MD4H3}

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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

3 papers in Pith

Perturbative QCD fitting of KEDR and BESIII $e^+e^-$ data for R(s) and $\alpha_s$ determination

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

Four-loop QCD mixing of current-current operators

Receipt and verification

First computed	2026-07-04T17:25:23.159183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddd178f88c350bee4eaf46faee307c3ecdd7b1a017deb2c98d486fa6afc86732

Aliases

arxiv: hep-ph/0411261 · arxiv_version: hep-ph/0411261v2 · doi: 10.48550/arxiv.hep-ph/0411261 · pith_short_12: 3XIXR6EMGUF6 · pith_short_16: 3XIXR6EMGUF64TVP · pith_short_8: 3XIXR6EM

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/3XIXR6EMGUF64TVPI35O4MD4H3 \
  | 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: ddd178f88c350bee4eaf46faee307c3ecdd7b1a017deb2c98d486fa6afc86732

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9007daaeef03a9d61850ad026589e04c8339f4c645289f64ca00771079d9c915",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2004-11-19T19:18:53Z",
    "title_canon_sha256": "13c3e074ffa14dd563f2abfcfb886835b7947a5e0629efa5f99d028549daeb2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0411261",
    "kind": "arxiv",
    "version": 2
  }
}