Pith Number

pith:CDX33TU7

pith:2011:CDX33TU74OJOGYUOVMLQY7ZEPY

not attested not anchored not stored refs pending

Logarithmic Gromov-Witten invariants

Bernd Siebert, Mark Gross

arxiv:1102.4322 v2 · 2011-02-21 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CDX33TU74OJOGYUOVMLQY7ZEPY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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.

Cited by

1 paper in Pith

Cut and paste invariants of moduli spaces of stable maps to toric surfaces

Receipt and verification

First computed	2026-05-18T03:43:18.913815Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10efbdce9fe392e3628eab170c7f247e3cb5c70fb64a1785f2a951090476c748

Aliases

arxiv: 1102.4322 · arxiv_version: 1102.4322v2 · doi: 10.48550/arxiv.1102.4322 · pith_short_12: CDX33TU74OJO · pith_short_16: CDX33TU74OJOGYUO · pith_short_8: CDX33TU7

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/CDX33TU74OJOGYUOVMLQY7ZEPY \
  | 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: 10efbdce9fe392e3628eab170c7f247e3cb5c70fb64a1785f2a951090476c748

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86246a7af98e087c13e2c207726c76b102db0357b593db156def48c7a3ceaa54",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-02-21T20:30:05Z",
    "title_canon_sha256": "bb9d6adc9138fb9c9cbebb423933f6d69c3497f141c8d6f40a9eeaf01bed372e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4322",
    "kind": "arxiv",
    "version": 2
  }
}