Pith Number

pith:CGT22OOK

pith:2013:CGT22OOKBPH5RDBKJFMUNUQAZN

not attested not anchored not stored refs pending

Enumeration of real curves in CP^{2n-1} and a WDVV relation for real Gromov-Witten invariants

Aleksey Zinger, Penka Georgieva

arxiv:1309.4079 v4 · 2013-09-16 · math.SG · 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{CGT22OOKBPH5RDBKJFMUNUQAZN}

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	2026-05-18T00:23:02.288552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11a7ad39ca0bcfd88c2a495946d200cb6cf26909722e827159f9b484d03a9911

Aliases

arxiv: 1309.4079 · arxiv_version: 1309.4079v4 · doi: 10.48550/arxiv.1309.4079 · pith_short_12: CGT22OOKBPH5 · pith_short_16: CGT22OOKBPH5RDBK · pith_short_8: CGT22OOK

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/CGT22OOKBPH5RDBKJFMUNUQAZN \
  | 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: 11a7ad39ca0bcfd88c2a495946d200cb6cf26909722e827159f9b484d03a9911

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4348e2f5f0fcd5890fdb1d652cd9ddc29f18baa730a7c49828086a2c1a20d699",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-09-16T19:40:31Z",
    "title_canon_sha256": "7acc7f46a9895333e7600b5c878f68e17b5380e88dca37aad0890a29ed9758ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.4079",
    "kind": "arxiv",
    "version": 4
  }
}