Pith Number

pith:MEXPJ65F

pith:2016:MEXPJ65F6DID6XMGT5F4LR2TJS

not attested not anchored not stored refs pending

Gopakumar-Vafa invariants via vanishing cycles

Davesh Maulik, Yukinobu Toda

arxiv:1610.07303 v4 · 2016-10-24 · math.AG · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MEXPJ65F6DID6XMGT5F4LR2TJS}

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

Large Order Enumerative Geometry, Black Holes and Black Rings

Receipt and verification

First computed	2026-05-18T00:19:47.780460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

612ef4fba5f0d03f5d869f4bc5c7534c8da4797fbe3c218650cadd7ab37df850

Aliases

arxiv: 1610.07303 · arxiv_version: 1610.07303v4 · doi: 10.48550/arxiv.1610.07303 · pith_short_12: MEXPJ65F6DID · pith_short_16: MEXPJ65F6DID6XMG · pith_short_8: MEXPJ65F

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/MEXPJ65F6DID6XMGT5F4LR2TJS \
  | 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: 612ef4fba5f0d03f5d869f4bc5c7534c8da4797fbe3c218650cadd7ab37df850

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac1bd9e73536d1350942aba9950297c060b2af19edded74bdad5ad46515e5511",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-10-24T07:15:16Z",
    "title_canon_sha256": "c5c45cb6617fbdc092e2f1d7b9cb89eaa1828d913d859663826b7f32c63783e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.07303",
    "kind": "arxiv",
    "version": 4
  }
}