Pith Number

pith:NGBLOUUP

pith:2018:NGBLOUUPJNEQSLVOFZ4ZGYMXH7

not attested not anchored not stored refs pending

Three-loop Euler-Heisenberg Lagrangian in 1+1 QED, part 1: single fermion-loop part

Christian Schubert, Idrish Huet, Michel Rausch de Traubenberg

arxiv:1812.08380 v1 · 2018-12-20 · hep-th · 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{NGBLOUUPJNEQSLVOFZ4ZGYMXH7}

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

Heisenberg-Euler and the Quantum Dilogarithm

Receipt and verification

First computed	2026-05-17T23:47:26.960294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6982b7528f4b49092eae2e799361973feaef8ad1c4e42ddb5ce6e3e7df5f48bc

Aliases

arxiv: 1812.08380 · arxiv_version: 1812.08380v1 · doi: 10.48550/arxiv.1812.08380 · pith_short_12: NGBLOUUPJNEQ · pith_short_16: NGBLOUUPJNEQSLVO · pith_short_8: NGBLOUUP

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/NGBLOUUPJNEQSLVOFZ4ZGYMXH7 \
  | 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: 6982b7528f4b49092eae2e799361973feaef8ad1c4e42ddb5ce6e3e7df5f48bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ed6ec9962b2b32be13d2fa282e23db6a3fc488047c7914c080981c56b81a6df",
    "cross_cats_sorted": [
      "hep-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2018-12-20T06:41:03Z",
    "title_canon_sha256": "1f95921e81cd464c32481f764dfa2cddd26a3d28ab3bcfbe4f6bf34105e22633"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.08380",
    "kind": "arxiv",
    "version": 1
  }
}