Pith Number

pith:TOOW4Q7J

pith:2000:TOOW4Q7JIRT3WTH3H66SFX2UJY

not attested not anchored not stored refs pending

Divergence operators and odd Poisson brackets

Juan Monterde, Yvette Kosmann-Schwarzbach

arxiv:math/0002209 v3 · 2000-02-25 · math.QA · math.RA · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TOOW4Q7JIRT3WTH3H66SFX2UJY}

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	2026-05-18T03:39:15.029286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b9d6e43e94467bb4cfb3fbd22df544e223be6f84c1ce6d5531a095e779b2fb6

Aliases

arxiv: math/0002209 · arxiv_version: math/0002209v3 · doi: 10.48550/arxiv.math/0002209 · pith_short_12: TOOW4Q7JIRT3 · pith_short_16: TOOW4Q7JIRT3WTH3 · pith_short_8: TOOW4Q7J

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/TOOW4Q7JIRT3WTH3H66SFX2UJY \
  | 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: 9b9d6e43e94467bb4cfb3fbd22df544e223be6f84c1ce6d5531a095e779b2fb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec2d88b6270247070e0f77dbd24fdaa0e492f6febfe963626f80842324314624",
    "cross_cats_sorted": [
      "math.RA",
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2000-02-25T08:26:49Z",
    "title_canon_sha256": "93f68c3683e8ad848d6b1170f97c3a434d227a781129fbef196cef9e50ea4b4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0002209",
    "kind": "arxiv",
    "version": 3
  }
}