Pith Number

pith:6GKQHR5F

pith:1993:6GKQHR5FKMW44BDHXM6HEYK7UJ

not attested not anchored not stored refs pending

The three-loop QCD $\beta$-function and anomalous dimensions

J.A.M. Vermaseren, S.A. Larin

arxiv:hep-ph/9302208 v1 · 1993-02-03 · hep-ph

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6GKQHR5FKMW44BDHXM6HEYK7UJ}

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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

5 papers in Pith

Optimization of perturbation series in QCD for physical quantities using the renormalization group: necessary conditions and partial results

Renormalisation

Slepton pair production at next-to-leading power

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

The strange and flavor-singlet axial form factors of the nucleon from lattice QCD

Receipt and verification

First computed	2026-05-18T04:22:50.918002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f19503c7a5532dce0467bb3c72615fa25ae4df6322faf6797e4d9e3909a41d09

Aliases

arxiv: hep-ph/9302208 · arxiv_version: hep-ph/9302208v1 · doi: 10.48550/arxiv.hep-ph/9302208 · pith_short_12: 6GKQHR5FKMW4 · pith_short_16: 6GKQHR5FKMW44BDH · pith_short_8: 6GKQHR5F

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/6GKQHR5FKMW44BDHXM6HEYK7UJ \
  | 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: f19503c7a5532dce0467bb3c72615fa25ae4df6322faf6797e4d9e3909a41d09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eac33e062092b2a930fe4bedf4d81602b189d15af4016893401d538d9e23ae18",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1993-02-03T14:26:25Z",
    "title_canon_sha256": "c5b4a2fadabf8d764d7ec7bbbc80342e7e86640e929c5d97d739f6a992e1be1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9302208",
    "kind": "arxiv",
    "version": 1
  }
}