Pith Number

pith:VMGD5G3J

pith:2007:VMGD5G3JXHRES5ZICV6XNOTDT6

not attested not anchored not stored refs pending

A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion

Dominique Manchon, Frederic Patras, Kurusch Ebrahimi-Fard

arxiv:0705.1265 v2 · 2007-05-09 · math.CO · hep-th · math-ph · math.MP · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VMGD5G3JXHRES5ZICV6XNOTDT6}

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	2026-05-17T23:49:18.315649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab0c3e9b69b9e2497728157d76ba639faf373ea3a3718bf1e03d73b3220497fe

Aliases

arxiv: 0705.1265 · arxiv_version: 0705.1265v2 · doi: 10.48550/arxiv.0705.1265 · pith_short_12: VMGD5G3JXHRE · pith_short_16: VMGD5G3JXHRES5ZI · pith_short_8: VMGD5G3J

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/VMGD5G3JXHRES5ZICV6XNOTDT6 \
  | 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: ab0c3e9b69b9e2497728157d76ba639faf373ea3a3718bf1e03d73b3220497fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8694b921a2379634267b69b26a31dcc85eabf7db46fae0e5d79c126f39a8eb02",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2007-05-09T11:51:03Z",
    "title_canon_sha256": "6a6164ca6c1a9aa5a9fd4eea5e7dce667722d48fd53484c272e90ff5098bdf6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0705.1265",
    "kind": "arxiv",
    "version": 2
  }
}