Pith Number

pith:VUBBFIM7

pith:1999:VUBBFIM7DNQV3CPVZO64L43355

not attested not anchored not stored refs pending

J-holomorphic curves, moment maps, and invariants of Hamiltonian group actions

Ana Rita Gaio, Dietmar A. Salamon, Kai Cieliebak

arxiv:math/9909122 v1 · 1999-09-21 · math.SG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VUBBFIM7DNQV3CPVZO64L43355}

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	2026-07-04T14:41:18.921096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad0212a19f1b615d89f5cbbdc5f37bef4e0c29bf73e5dc330524e6f29a6671d7

Aliases

arxiv: math/9909122 · arxiv_version: math/9909122v1 · doi: 10.48550/arxiv.math/9909122 · pith_short_12: VUBBFIM7DNQV · pith_short_16: VUBBFIM7DNQV3CPV · pith_short_8: VUBBFIM7

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/VUBBFIM7DNQV3CPVZO64L43355 \
  | 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: ad0212a19f1b615d89f5cbbdc5f37bef4e0c29bf73e5dc330524e6f29a6671d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb83886612eb52130d53e6b02e94f3087b126b2ce72fe3a2492389c4018de547",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.SG",
    "submitted_at": "1999-09-21T19:15:23Z",
    "title_canon_sha256": "86966d79b437b50a2a0dba8c7b4da22add58e65997ce4ee00d9148c0909e0338"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9909122",
    "kind": "arxiv",
    "version": 1
  }
}