Pith Number

pith:4BKMPOSI

pith:2005:4BKMPOSIC2TYCSNP5RRD47RWYO

not attested not anchored not stored refs pending

Renormalization-group improved evolution of the meson distribution amplitude at the two-loop level

Alexander P. Bakulev, N. G. Stefanis

arxiv:hep-ph/0503045 v3 · 2005-03-04 · 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{4BKMPOSIC2TYCSNP5RRD47RWYO}

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	2026-07-04T15:22:25.420464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e054c7ba4816a78149afec623e7e36c3845c1264521c6e342160315aa3ec0418

Aliases

arxiv: hep-ph/0503045 · arxiv_version: hep-ph/0503045v3 · doi: 10.48550/arxiv.hep-ph/0503045 · pith_short_12: 4BKMPOSIC2TY · pith_short_16: 4BKMPOSIC2TYCSNP · pith_short_8: 4BKMPOSI

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/4BKMPOSIC2TYCSNP5RRD47RWYO \
  | 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: e054c7ba4816a78149afec623e7e36c3845c1264521c6e342160315aa3ec0418

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58c8e40c14b9a7d25764765782099417224b75f40543e3415c2b63ccbb5bcaef",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2005-03-04T11:43:05Z",
    "title_canon_sha256": "c03a14a55ed4b97e845f6dc9f7bf9ba4ebf61e2da65353ebdba069daeddeab63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0503045",
    "kind": "arxiv",
    "version": 3
  }
}