Pith Number

pith:72ELZJ5D

pith:1999:72ELZJ5DNJMVUVPQYWV7AHRM4G

not attested not anchored not stored refs pending

Absolute and relative Gromov-Witten invariants of very ample hypersurfaces

Andreas Gathmann

arxiv:math/9908054 v1 · 1999-08-12 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{72ELZJ5DNJMVUVPQYWV7AHRM4G}

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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-04T14:41:16.251446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe88bca7a36a595a55f0c5abf01e2ce1aa4778f1037a0edd8dc40550c52ebcfd

Aliases

arxiv: math/9908054 · arxiv_version: math/9908054v1 · doi: 10.48550/arxiv.math/9908054 · pith_short_12: 72ELZJ5DNJMV · pith_short_16: 72ELZJ5DNJMVUVPQ · pith_short_8: 72ELZJ5D

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/72ELZJ5DNJMVUVPQYWV7AHRM4G \
  | 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: fe88bca7a36a595a55f0c5abf01e2ce1aa4778f1037a0edd8dc40550c52ebcfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d585f6b8666aac65ee06478f8bc2d1c91d9c3342cae457f88e2a03695a25aea2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "1999-08-12T01:54:55Z",
    "title_canon_sha256": "a072712c9447aecb8224096edf391f4e483c99b7216686ee3f9dc14e77f95d79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9908054",
    "kind": "arxiv",
    "version": 1
  }
}