Pith Number

pith:MP4BDPXT

pith:2007:MP4BDPXTSO25VV45ZQEYMYXFAE

not attested not anchored not stored refs pending

Modular classes of Lie algebroid morphisms

Alan Weinstein, Camille Laurent-Gengoux, Yvette Kosmann-Schwarzbach

arxiv:0712.3021 v2 · 2007-12-18 · 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{MP4BDPXTSO25VV45ZQEYMYXFAE}

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	2026-07-04T15:10:56.526013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63f811bef393b5dad79dcc098662e501340eeb094095cf12db399311dcee428d

Aliases

arxiv: 0712.3021 · arxiv_version: 0712.3021v2 · doi: 10.48550/arxiv.0712.3021 · pith_short_12: MP4BDPXTSO25 · pith_short_16: MP4BDPXTSO25VV45 · pith_short_8: MP4BDPXT

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/MP4BDPXTSO25VV45ZQEYMYXFAE \
  | 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: 63f811bef393b5dad79dcc098662e501340eeb094095cf12db399311dcee428d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a5eaae53aac157bf72482daff69f50fd0c3a175bbcb8710a96497a9269c82dd",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2007-12-18T18:50:04Z",
    "title_canon_sha256": "4e7ca8c6a1bbf97a122de95255f98bd26a1e68a38fe4481a201bd6d299b158f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3021",
    "kind": "arxiv",
    "version": 2
  }
}