Pith Number

pith:YD6P6VAY

pith:2014:YD6P6VAYY65D4IDNZ3R2F3JMI7

not attested not anchored not stored refs pending

Non-commutative width and Gopakumar-Vafa invariants

Yukinobu Toda

arxiv:1411.1505 v1 · 2014-11-06 · 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{YD6P6VAYY65D4IDNZ3R2F3JMI7}

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	2026-05-18T02:38:27.734212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0fcff5418c7ba3e206dcee3a2ed2c47e2e3c47bf25e6be29771afdac1ff5cc8

Aliases

arxiv: 1411.1505 · arxiv_version: 1411.1505v1 · doi: 10.48550/arxiv.1411.1505 · pith_short_12: YD6P6VAYY65D · pith_short_16: YD6P6VAYY65D4IDN · pith_short_8: YD6P6VAY

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/YD6P6VAYY65D4IDNZ3R2F3JMI7 \
  | 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: c0fcff5418c7ba3e206dcee3a2ed2c47e2e3c47bf25e6be29771afdac1ff5cc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8559720d6eff4e75586b2ff7c2391c152445e751ac0d1dc6cd06ede0f794eac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2014-11-06T05:41:30Z",
    "title_canon_sha256": "f5ef37edc7d1b054f2d339b7028c6183fe295115d8b6dab139812ec475dc301f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.1505",
    "kind": "arxiv",
    "version": 1
  }
}