Pith Number

pith:IJACJVE4

pith:2013:IJACJVE4V7PUAG7R3CTSAV64CM

not attested not anchored not stored refs pending

The Gopakumar-Vafa formula for symplectic manifolds

Eleny-Nicoleta Ionel, Thomas H. Parker

arxiv:1306.1516 v6 · 2013-06-06 · 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{IJACJVE4V7PUAG7R3CTSAV64CM}

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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

Large Order Enumerative Geometry, Black Holes and Black Rings

Receipt and verification

First computed	2026-05-18T00:33:33.099170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

424024d49cafdf401bf1d8a72057dc1324112e9e2c15a77e972eb26d80213989

Aliases

arxiv: 1306.1516 · arxiv_version: 1306.1516v6 · doi: 10.48550/arxiv.1306.1516 · pith_short_12: IJACJVE4V7PU · pith_short_16: IJACJVE4V7PUAG7R · pith_short_8: IJACJVE4

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/IJACJVE4V7PUAG7R3CTSAV64CM \
  | 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: 424024d49cafdf401bf1d8a72057dc1324112e9e2c15a77e972eb26d80213989

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "358068ae2ca5e6f509d0d5d5b61f8f6f195c6dcd3130c5213d7128392e23db0f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-06-06T19:19:17Z",
    "title_canon_sha256": "dd1680c23a2645dd28835e868a16e9547a833e08c17a0fcb6fc843273dd8c0fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1516",
    "kind": "arxiv",
    "version": 6
  }
}