Pith Number

pith:UTR5ZNG4

pith:2001:UTR5ZNG4PDBHJH7EZMER4F4F26

not attested not anchored not stored refs pending

Dynamical renormalization group approach to the Altarelli-Parisi-Lipatov equations

D. Boyanovsky, D.-S. Lee, H. J. de Vega, H.-L. Yu, S.-Y. Wang

arxiv:hep-ph/0108180 v2 · 2001-08-22 · 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{UTR5ZNG4PDBHJH7EZMER4F4F26}

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	2026-05-18T02:36:39.435743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4e3dcb4dc78c2749fe4cb091e1785d7891cc2a047014be5fb79c0b6848aa7f3

Aliases

arxiv: hep-ph/0108180 · arxiv_version: hep-ph/0108180v2 · doi: 10.48550/arxiv.hep-ph/0108180 · pith_short_12: UTR5ZNG4PDBH · pith_short_16: UTR5ZNG4PDBHJH7E · pith_short_8: UTR5ZNG4

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/UTR5ZNG4PDBHJH7EZMER4F4F26 \
  | 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: a4e3dcb4dc78c2749fe4cb091e1785d7891cc2a047014be5fb79c0b6848aa7f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa42ed1174f845db83afd5d02e4370667b369a62703afff224876b0bacea2e42",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2001-08-22T18:48:36Z",
    "title_canon_sha256": "86c43c0f0b78d2a3e7dbddec6510fcb8d50ed94b867df8cb358f18aac4890606"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0108180",
    "kind": "arxiv",
    "version": 2
  }
}