Pith Number

pith:XD5MRUSX

pith:2013:XD5MRUSXPV7KYXLOTNHZQWR333

not attested not anchored not stored refs pending

Perturbative series and the 1/N expansion for the QED \beta-function

S.A. Larin

arxiv:1310.6388 v1 · 2013-10-16 · 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{XD5MRUSXPV7KYXLOTNHZQWR333}

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.

Receipt and verification

First computed	2026-05-18T02:32:46.385590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8fac8d2577d7eac5d6e9b4f985a3bdeea512e29661313bbdc5cfd3a09c56379

Aliases

arxiv: 1310.6388 · arxiv_version: 1310.6388v1 · doi: 10.48550/arxiv.1310.6388 · pith_short_12: XD5MRUSXPV7K · pith_short_16: XD5MRUSXPV7KYXLO · pith_short_8: XD5MRUSX

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/XD5MRUSXPV7KYXLOTNHZQWR333 \
  | 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: b8fac8d2577d7eac5d6e9b4f985a3bdeea512e29661313bbdc5cfd3a09c56379

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ea66d07b8536c0355b19b3cb3c593857f847898dae9e34c10f92bc9c1b93242",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2013-10-16T16:18:26Z",
    "title_canon_sha256": "0e62625a1d8ddf8c51fe06b4d1b73488f0d40483339455ff6cdf9b424b3f9a85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6388",
    "kind": "arxiv",
    "version": 1
  }
}