Pith Number

pith:S2QFWZGK

pith:2012:S2QFWZGK22BAI42CNE4D2AOUIE

not attested not anchored not stored refs pending

Anomalous dimensions of gauge fields and gauge coupling beta-functions in the Standard Model at three loops

A. F. Pikelner, A. V. Bednyakov, V. N. Velizhanin

arxiv:1210.6873 v4 · 2012-10-25 · 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{S2QFWZGK22BAI42CNE4D2AOUIE}

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	2026-05-18T03:30:25.479034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96a05b64cad68204734269383d01d4412f5bf7d354ffc676d6b7498f0565aacb

Aliases

arxiv: 1210.6873 · arxiv_version: 1210.6873v4 · doi: 10.48550/arxiv.1210.6873 · pith_short_12: S2QFWZGK22BA · pith_short_16: S2QFWZGK22BAI42C · pith_short_8: S2QFWZGK

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/S2QFWZGK22BAI42CNE4D2AOUIE \
  | 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: 96a05b64cad68204734269383d01d4412f5bf7d354ffc676d6b7498f0565aacb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9da42e91f1b886bd7234866d55e2cc023a64878b9a11f7b2cd24b609352a8544",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2012-10-25T15:18:51Z",
    "title_canon_sha256": "04f11786ac21729d45a4f037efe583a5676efaf00a928d5ebd481f34e912a946"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6873",
    "kind": "arxiv",
    "version": 4
  }
}