Pith Number

pith:5QDM7MUA

pith:2006:5QDM7MUAOMX3H3Y3S7Q5NJWSRI

not attested not anchored not stored refs pending

Two-Loop Renormalization in the Standard Model Part III: Renormalization Equations and their Solutions

G. Passarino, S. Actis

arxiv:hep-ph/0612124 v1 · 2006-12-11 · 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{5QDM7MUAOMX3H3Y3S7Q5NJWSRI}

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

Towards the two-loop electroweak corrections to the Drell-Yan process: the complete fermionic contributions

Receipt and verification

First computed	2026-07-04T15:18:52.195213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec06cfb280732fb3ef1b97e1d6a6d28a275e26da2a01633937b839e46426de86

Aliases

arxiv: hep-ph/0612124 · arxiv_version: hep-ph/0612124v1 · doi: 10.48550/arxiv.hep-ph/0612124 · pith_short_12: 5QDM7MUAOMX3 · pith_short_16: 5QDM7MUAOMX3H3Y3 · pith_short_8: 5QDM7MUA

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/5QDM7MUAOMX3H3Y3S7Q5NJWSRI \
  | 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: ec06cfb280732fb3ef1b97e1d6a6d28a275e26da2a01633937b839e46426de86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c94c519756ae81f911eda961f30417b836a040a7da44768a947b37572464be1",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2006-12-11T12:31:54Z",
    "title_canon_sha256": "6643ded104dab4bb975d89ae6a897e27442810215733ed237b5863d2cf65f3f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0612124",
    "kind": "arxiv",
    "version": 1
  }
}