Pith Number

pith:CEO2QMT2

pith:2005:CEO2QMT2F4WTC72EJURX4MD7GH

not attested not anchored not stored refs pending

Relative modular classes of Lie algebroids

Alan Weinstein, Yvette Kosmann-Schwarzbach

arxiv:math/0508515 v1 · 2005-08-25 · math.DG · 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{CEO2QMT2F4WTC72EJURX4MD7GH}

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	2026-07-04T14:40:20.292393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

111da8327a2f2d317f444d237e307f31c63b526420989f038b6ce466d6179848

Aliases

arxiv: math/0508515 · arxiv_version: math/0508515v1 · doi: 10.48550/arxiv.math/0508515 · pith_short_12: CEO2QMT2F4WT · pith_short_16: CEO2QMT2F4WTC72E · pith_short_8: CEO2QMT2

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/CEO2QMT2F4WTC72EJURX4MD7GH \
  | 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: 111da8327a2f2d317f444d237e307f31c63b526420989f038b6ce466d6179848

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62c9042c55ca719067277e08420d6567b3b15cfed3f54f682c07ac59e384b246",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2005-08-25T17:58:55Z",
    "title_canon_sha256": "dad624e5e460a2ee1f177265b1836924b17b8c199ebf24e2cb352be11e0f807a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508515",
    "kind": "arxiv",
    "version": 1
  }
}