Pith Number

pith:WNTV4LJ4

pith:2017:WNTV4LJ4IM5KKG7NJVH7Q4ZZWI

not attested not anchored not stored refs pending

Gopakumar-Vafa invariants and wall-crossing

Yukinobu Toda

arxiv:1710.01843 v4 · 2017-10-05 · math.AG · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WNTV4LJ4IM5KKG7NJVH7Q4ZZWI}

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

$\chi$-independence for K3-surfaces via $p$-adic integration

Receipt and verification

First computed	2026-07-05T03:54:15.282602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3675e2d3c433aa51bed4d4ff87339b23a2f7b0776930523f9ca8b09ea01a45f

Aliases

arxiv: 1710.01843 · arxiv_version: 1710.01843v4 · doi: 10.48550/arxiv.1710.01843 · pith_short_12: WNTV4LJ4IM5K · pith_short_16: WNTV4LJ4IM5KKG7N · pith_short_8: WNTV4LJ4

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/WNTV4LJ4IM5KKG7NJVH7Q4ZZWI \
  | 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: b3675e2d3c433aa51bed4d4ff87339b23a2f7b0776930523f9ca8b09ea01a45f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78a2e1d789d2e29925f643ecf64bbb196248113649d8fd60ecfb515d4b6cf329",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-10-05T00:58:34Z",
    "title_canon_sha256": "1c41f67c2d5901fcbf0756d941c35686f5e2426a7ff1c68a5f49c36d0e6543d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.01843",
    "kind": "arxiv",
    "version": 4
  }
}