Pith Number

pith:VMKPYQDY

pith:2011:VMKPYQDYN2UTV3CF2IFYTNBHJQ

not attested not anchored not stored refs pending

Two-loop QED Operator Matrix Elements with Massive External Fermion Lines

Abilio De Freitas, Johannes Bl\"umlein, Wilhelmus van Neerven

arxiv:1107.4638 v1 · 2011-07-22 · 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{VMKPYQDYN2UTV3CF2IFYTNBHJQ}

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

Optimization of factorization scale in QED Drell-Yan-like processes

Receipt and verification

First computed	2026-05-18T04:09:46.790668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab14fc40786ea93aec45d20b89b4274c2902cbb9fefeada85096e490dd2e86a4

Aliases

arxiv: 1107.4638 · arxiv_version: 1107.4638v1 · doi: 10.48550/arxiv.1107.4638 · pith_short_12: VMKPYQDYN2UT · pith_short_16: VMKPYQDYN2UTV3CF · pith_short_8: VMKPYQDY

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/VMKPYQDYN2UTV3CF2IFYTNBHJQ \
  | 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: ab14fc40786ea93aec45d20b89b4274c2902cbb9fefeada85096e490dd2e86a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89cc36248534f00835fe78db39b29178431405b2d5017099e6e9629c63502f1b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2011-07-22T22:18:28Z",
    "title_canon_sha256": "07175dd514ff6e89269d86cba6a4728c7c4675bc5d862637919a4097f380efc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4638",
    "kind": "arxiv",
    "version": 1
  }
}