Pith Number

pith:BUEP5ZPK

pith:2024:BUEP5ZPKVPWGOX2LXTENL7HQWL

not attested not anchored not stored refs pending

Three-loop ladder diagrams with two off-shell legs

Ming-Ming Long

arxiv:2410.15431 v2 · 2024-10-20 · 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{BUEP5ZPKVPWGOX2LXTENL7HQWL}

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

LINE: Loop Integrals Numerical Evaluation

Receipt and verification

First computed	2026-07-05T09:53:06.559459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d08fee5eaabec675f4bbcc8d5fcf0b2d54d0c48bc144ab8706a113ac906fd96

Aliases

arxiv: 2410.15431 · arxiv_version: 2410.15431v2 · doi: 10.48550/arxiv.2410.15431 · pith_short_12: BUEP5ZPKVPWG · pith_short_16: BUEP5ZPKVPWGOX2L · pith_short_8: BUEP5ZPK

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/BUEP5ZPKVPWGOX2LXTENL7HQWL \
  | 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: 0d08fee5eaabec675f4bbcc8d5fcf0b2d54d0c48bc144ab8706a113ac906fd96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "845e67a3ff7b695e032f7b6784999b4bc8b12c3b33d1f88bdf7edfd8800e1357",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2024-10-20T15:59:58Z",
    "title_canon_sha256": "b92fce27b99409b879f32b0309c59718d2efe4e277e680e0c408419371c4a0b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.15431",
    "kind": "arxiv",
    "version": 2
  }
}