Pith Number

pith:ZKDPQ6LY

pith:2006:ZKDPQ6LY3O7NJIPJPUGDA45S5Y

not attested not anchored not stored refs pending

Two-Loop Vertices in Quantum Field Theory: Infrared and Collinear Divergent Configurations

Giampiero Passarino, Sandro Uccirati

arxiv:hep-ph/0603121 v1 · 2006-03-16 · 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{ZKDPQ6LY3O7NJIPJPUGDA45S5Y}

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

Numerical computation of Fox functions

Receipt and verification

First computed	2026-07-04T17:01:41.806127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca86f87978dbbed4a1e97d0c3073b2ee0c4f777da5b4a771c8bfdee519979410

Aliases

arxiv: hep-ph/0603121 · arxiv_version: hep-ph/0603121v1 · doi: 10.48550/arxiv.hep-ph/0603121 · pith_short_12: ZKDPQ6LY3O7N · pith_short_16: ZKDPQ6LY3O7NJIPJ · pith_short_8: ZKDPQ6LY

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/ZKDPQ6LY3O7NJIPJPUGDA45S5Y \
  | 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: ca86f87978dbbed4a1e97d0c3073b2ee0c4f777da5b4a771c8bfdee519979410

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8107950aa14cfaffd3e169c928de9c538f3ae541a3fd9e6caa0b2f042a3a8728",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2006-03-16T14:12:42Z",
    "title_canon_sha256": "d93bf65325bbfe4002db81b2acd1a71a80c4403f887dd65ed1889f654e1bca9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0603121",
    "kind": "arxiv",
    "version": 1
  }
}