Pith Number

pith:XLUSPLDL

pith:2005:XLUSPLDLYBYPRKBL33E2AYX3E3

not attested not anchored not stored refs pending

QCD Analytic Perturbation Theory. From integer powers to any power of the running coupling

A. P. Bakulev, N. G. Stefanis, S. V. Mikhailov

arxiv:hep-ph/0506311 v3 · 2005-06-29 · hep-ph · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XLUSPLDLYBYPRKBL33E2AYX3E3}

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.

Cited by

1 paper in Pith

Renormalon-based resummation for B(D) Mesons

Receipt and verification

First computed	2026-05-18T02:36:19.676233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bae927ac6bc070f8a82bdec9a062fb26fcf8b741db37551ceeede8f1b7b42d46

Aliases

arxiv: hep-ph/0506311 · arxiv_version: hep-ph/0506311v3 · doi: 10.48550/arxiv.hep-ph/0506311 · pith_short_12: XLUSPLDLYBYP · pith_short_16: XLUSPLDLYBYPRKBL · pith_short_8: XLUSPLDL

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/XLUSPLDLYBYPRKBL33E2AYX3E3 \
  | 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: bae927ac6bc070f8a82bdec9a062fb26fcf8b741db37551ceeede8f1b7b42d46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6600dbfd862155151d55f92bd7c1420831e9fa8a1b8ccc33df3c0791a96a76cd",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2005-06-29T18:59:58Z",
    "title_canon_sha256": "487a137ab8b0b97875fea7c4aa24ff8838164160cc8f367f453a3e4e20bf9c0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0506311",
    "kind": "arxiv",
    "version": 3
  }
}