Pith Number

pith:XBIOSRAF

pith:2002:XBIOSRAFCXXJP75N6XNBMSJCWE

not attested not anchored not stored refs pending

Two-loop Renormalization Group Equations in General Gauge Field Theories

Huawen Wang, Mingxing Luo, Yong Xiao (zhejiang University)

arxiv:hep-ph/0211440 v3 · 2002-11-28 · 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{XBIOSRAFCXXJP75N6XNBMSJCWE}

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

2 papers in Pith

Imaginary scaling invariance of the one-loop effective potential

Renormalisation and invariants for two U(1)s

Receipt and verification

First computed	2026-07-04T16:34:28.380689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b850e9440515ee97ffadf5da164922b11e3c87ef214e03481c28f7c3ccf18a19

Aliases

arxiv: hep-ph/0211440 · arxiv_version: hep-ph/0211440v3 · doi: 10.48550/arxiv.hep-ph/0211440 · pith_short_12: XBIOSRAFCXXJ · pith_short_16: XBIOSRAFCXXJP75N · pith_short_8: XBIOSRAF

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/XBIOSRAFCXXJP75N6XNBMSJCWE \
  | 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: b850e9440515ee97ffadf5da164922b11e3c87ef214e03481c28f7c3ccf18a19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "389d1a75667b87174a85e117c1bdbdbda6132dacc0f1afb6f1720f4bc22b3185",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2002-11-28T08:02:07Z",
    "title_canon_sha256": "899e9d851915d68d624f6d4cd650ffb9bc214dfa64af17f6d590da8811582808"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0211440",
    "kind": "arxiv",
    "version": 3
  }
}