Pith Number

pith:PMI7I6ZF

pith:2015:PMI7I6ZFXIR77DPHGAL55XQZCP

not attested not anchored not stored refs pending

A remark on virtual pushforward properties in Gromov-Witten theory

F. Qu

arxiv:1511.09028 v2 · 2015-11-29 · 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{PMI7I6ZFXIR77DPHGAL55XQZCP}

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

Gopakumar-Vafa invariants of fiber classes on Calabi-Yau 4-folds fibered over curves

Receipt and verification

First computed	2026-05-18T01:07:54.001602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b11f47b25ba23ff8de73017dede1913f2cf6c6b8849d106086d1d71534a39d3

Aliases

arxiv: 1511.09028 · arxiv_version: 1511.09028v2 · doi: 10.48550/arxiv.1511.09028 · pith_short_12: PMI7I6ZFXIR7 · pith_short_16: PMI7I6ZFXIR77DPH · pith_short_8: PMI7I6ZF

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/PMI7I6ZFXIR77DPHGAL55XQZCP \
  | 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: 7b11f47b25ba23ff8de73017dede1913f2cf6c6b8849d106086d1d71534a39d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7213b9a4ef28f02a42de6a4e290adb59a8986b14e15eb74b4406a6e88fa94301",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-11-29T15:42:30Z",
    "title_canon_sha256": "47f02e06be5a6e2054f3aa5bd4535b45c46f2e2d1d6cc84b3ccff447c6e36f4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.09028",
    "kind": "arxiv",
    "version": 2
  }
}