Pith Number

pith:2I4C2IVW

pith:2000:2I4C2IVWXBCJ36QD3D5DLAVR7X

not attested not anchored not stored refs pending

Three-loop Three-Linear Vertices and Four-Loop MOM beta functions in massless QCD

A. Retey (U. of Karlsruhe), K.G. Chetyrkin (U. of Freiburg, U. of Karlsruhe)

arxiv:hep-ph/0007088 v1 · 2000-07-10 · 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{2I4C2IVWXBCJ36QD3D5DLAVR7X}

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

1 paper in Pith

Renormalisation

Receipt and verification

First computed	2026-07-04T14:27:37.690293Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2382d22b6b8449dfa03d8fa3582b1fdc30acda8d1e3958930080a6202ca9bbf

Aliases

arxiv: hep-ph/0007088 · arxiv_version: hep-ph/0007088v1 · doi: 10.48550/arxiv.hep-ph/0007088 · pith_short_12: 2I4C2IVWXBCJ · pith_short_16: 2I4C2IVWXBCJ36QD · pith_short_8: 2I4C2IVW

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/2I4C2IVWXBCJ36QD3D5DLAVR7X \
  | 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: d2382d22b6b8449dfa03d8fa3582b1fdc30acda8d1e3958930080a6202ca9bbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4870686265df63aef1524c3244066efb37bcb8644e4846ffbb1e606f03891c2c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2000-07-10T18:40:40Z",
    "title_canon_sha256": "842bda15424aba444109f6c4fa2d2738f67877095442701b752f66e2b1ae4993"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0007088",
    "kind": "arxiv",
    "version": 1
  }
}