Pith Number

pith:MLMFUXKS

pith:1999:MLMFUXKSSKSA4V2AOTJ3J3MSHW

not attested not anchored not stored refs pending

Explicit Calculation Of the Running Coupling BFKL Anomalous Dimension

R.S. Thorne

arxiv:hep-ph/9912284 v1 · 1999-12-09 · 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{MLMFUXKSSKSA4V2AOTJ3J3MSHW}

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	2026-07-04T16:14:35.251063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62d85a5d5292a40e574074d3b4ed923dbf5a0d1fda95047b0e93986b6dc25c82

Aliases

arxiv: hep-ph/9912284 · arxiv_version: hep-ph/9912284v1 · doi: 10.48550/arxiv.hep-ph/9912284 · pith_short_12: MLMFUXKSSKSA · pith_short_16: MLMFUXKSSKSA4V2A · pith_short_8: MLMFUXKS

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/MLMFUXKSSKSA4V2AOTJ3J3MSHW \
  | 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: 62d85a5d5292a40e574074d3b4ed923dbf5a0d1fda95047b0e93986b6dc25c82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fbe7c3b2a8d7b32980a3bf9f70e8e09790bad42de77f1453bcfb8ea6c42216b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1999-12-09T21:20:32Z",
    "title_canon_sha256": "3da597c570d31f89b33ef9edac2109cc3183238ec983dd55905a855bf3a8f309"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9912284",
    "kind": "arxiv",
    "version": 1
  }
}