Pith Number

pith:IAPE7EXM

pith:2010:IAPE7EXMS4JD5W6QNIH6A7N3FE

not attested not anchored not stored refs pending

A Normal Form Theorem around Symplectic Leaves

Ioan Marcut, Marius Crainic

arxiv:1009.2090 v3 · 2010-09-10 · 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{IAPE7EXMS4JD5W6QNIH6A7N3FE}

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	2026-05-18T03:39:42.199649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

401e4f92ec97123edbd06a0fe07dbb290939608b054ccf2f2433b9dab5993272

Aliases

arxiv: 1009.2090 · arxiv_version: 1009.2090v3 · doi: 10.48550/arxiv.1009.2090 · pith_short_12: IAPE7EXMS4JD · pith_short_16: IAPE7EXMS4JD5W6Q · pith_short_8: IAPE7EXM

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/IAPE7EXMS4JD5W6QNIH6A7N3FE \
  | 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: 401e4f92ec97123edbd06a0fe07dbb290939608b054ccf2f2433b9dab5993272

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5145ba50c18ffa58fc7124a3ce1e67b514b08c00c91b66174da8553fc5e9999d",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-09-10T20:03:39Z",
    "title_canon_sha256": "e2370153eb41587e70571a494287d91982e105aac24eff8b531cefb366d1caab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2090",
    "kind": "arxiv",
    "version": 3
  }
}