Pith Number

pith:RW4BME4E

pith:2001:RW4BME4EFS7ADAUKGXCS53VM2H

not attested not anchored not stored refs pending

Factorization and Resummation of Small x Scaling Violations with Running Coupling

Guido Altarelli, Richard D. Ball, Stefano Forte

arxiv:hep-ph/0109178 v1 · 2001-09-20 · 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{RW4BME4EFS7ADAUKGXCS53VM2H}

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	2026-07-04T15:20:48.837492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8db81613842cbe01828a35c52eeeacd1ff1f74c8771c08960f95c58a79ac9082

Aliases

arxiv: hep-ph/0109178 · arxiv_version: hep-ph/0109178v1 · doi: 10.48550/arxiv.hep-ph/0109178 · pith_short_12: RW4BME4EFS7A · pith_short_16: RW4BME4EFS7ADAUK · pith_short_8: RW4BME4E

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/RW4BME4EFS7ADAUKGXCS53VM2H \
  | 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: 8db81613842cbe01828a35c52eeeacd1ff1f74c8771c08960f95c58a79ac9082

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef856e61a22b29d8beb01c6bf16157db7466106b49993a99c486fd72edae55b4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2001-09-20T09:27:22Z",
    "title_canon_sha256": "4c3d0f66b1df438a7d3e51e52a74c10595bc94bbd162baabc62acbd0193f82ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0109178",
    "kind": "arxiv",
    "version": 1
  }
}