Pith Number

pith:KPUXFAD4

pith:2002:KPUXFAD4LWNZ7APG3DS4F5EXXL

not attested not anchored not stored refs pending

Two-loop Renormalization Group Equations in the Standard Model

Mingxing Luo, Yong Xiao (Zhejiang U.)

arxiv:hep-ph/0207271 v2 · 2002-07-23 · 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{KPUXFAD4LWNZ7APG3DS4F5EXXL}

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

Three-loop corrections to the Fermi decay constant in the $\overline{\rm{MS}}$ scheme

Receipt and verification

First computed	2026-07-04T16:34:16.383141Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53e972807c5d9b9f81e6d8e5c2f497bae9d0bdecb34d272854ec2b12934eb40c

Aliases

arxiv: hep-ph/0207271 · arxiv_version: hep-ph/0207271v2 · doi: 10.48550/arxiv.hep-ph/0207271 · pith_short_12: KPUXFAD4LWNZ · pith_short_16: KPUXFAD4LWNZ7APG · pith_short_8: KPUXFAD4

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/KPUXFAD4LWNZ7APG3DS4F5EXXL \
  | 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: 53e972807c5d9b9f81e6d8e5c2f497bae9d0bdecb34d272854ec2b12934eb40c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17c761bcd0c40638efeca7b385d5d0b80b34919537b0d3f01b91f259757c033f",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2002-07-23T04:26:16Z",
    "title_canon_sha256": "19ee100f8c01fd6cbd841bb4c336b46cbf1b363a92ce71dafa1a95efbe0dd8eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0207271",
    "kind": "arxiv",
    "version": 2
  }
}