Pith Number

pith:PMF4U2CE

pith:2004:PMF4U2CESJNY6BW5F2JH2DMVSN

not attested not anchored not stored refs pending

Mathematical Structure of Anomalous Dimensions and QCD Wilson Coefficients in Higher Order

J. Bl\"umlein

arxiv:hep-ph/0407044 v1 · 2004-07-04 · hep-ph · hep-th · math.NT · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PMF4U2CESJNY6BW5F2JH2DMVSN}

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	2026-07-04T16:48:17.901876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b0bca6844925b8f06dd2e927d0d959345c13b72bfc3a3ebc1a3ba39671c9c09

Aliases

arxiv: hep-ph/0407044 · arxiv_version: hep-ph/0407044v1 · doi: 10.48550/arxiv.hep-ph/0407044 · pith_short_12: PMF4U2CESJNY · pith_short_16: PMF4U2CESJNY6BW5 · pith_short_8: PMF4U2CE

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/PMF4U2CESJNY6BW5F2JH2DMVSN \
  | 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: 7b0bca6844925b8f06dd2e927d0d959345c13b72bfc3a3ebc1a3ba39671c9c09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e401c6b509d88f4f45a5dcbc025e278291f24b743d40fa13f13a6622d830368",
    "cross_cats_sorted": [
      "hep-th",
      "math.NT",
      "math.QA"
    ],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2004-07-04T14:25:23Z",
    "title_canon_sha256": "ec5daf6eab3f926917324e8854dd4f2577d8c616a9c99c3bc17b14323d2456de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0407044",
    "kind": "arxiv",
    "version": 1
  }
}