Pith Number

pith:NHHMHX6Y

pith:1999:NHHMHX6YVWFPUTPKDTVFLYZ6VA

not attested not anchored not stored refs pending

NLO BFKL Equation, Running Coupling and Renormalization Scales

R.S. Thorne

arxiv:hep-ph/9901331 v2 · 1999-01-17 · 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{NHHMHX6YVWFPUTPKDTVFLYZ6VA}

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	2026-07-04T16:14:03.302124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69cec3dfd8ad8afa4dea1cea55e33ea8059cdd9d1eca9f6b51e076bac1a83349

Aliases

arxiv: hep-ph/9901331 · arxiv_version: hep-ph/9901331v2 · doi: 10.48550/arxiv.hep-ph/9901331 · pith_short_12: NHHMHX6YVWFP · pith_short_16: NHHMHX6YVWFPUTPK · pith_short_8: NHHMHX6Y

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/NHHMHX6YVWFPUTPKDTVFLYZ6VA \
  | 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: 69cec3dfd8ad8afa4dea1cea55e33ea8059cdd9d1eca9f6b51e076bac1a83349

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3d3855f67aecce35772bbcfbfefcba9de0400fb95a4417a5e9b35d1154e169f",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1999-01-17T15:25:18Z",
    "title_canon_sha256": "5cde16a1997105a6ff750adebc8bbe8fe20603e8371c4420b305a306334e2144"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9901331",
    "kind": "arxiv",
    "version": 2
  }
}