Pith Number

pith:X6ZF6XJO

pith:2011:X6ZF6XJOHNPP2DMPAM4MW6OMBU

not attested not anchored not stored refs pending

The Calabi-Yau property of Hopf algebras and braided Hopf algebras

Xiaolan Yu, Yinhuo Zhang

arxiv:1111.4201 v1 · 2011-11-17 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X6ZF6XJOHNPP2DMPAM4MW6OMBU}

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	2026-05-18T04:08:05.492466Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfb25f5d2e3b5efd0d8f0338cb79cc0d3e3eed48d83d902a15919d0654f1eb1d

Aliases

arxiv: 1111.4201 · arxiv_version: 1111.4201v1 · doi: 10.48550/arxiv.1111.4201 · pith_short_12: X6ZF6XJOHNPP · pith_short_16: X6ZF6XJOHNPP2DMP · pith_short_8: X6ZF6XJO

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/X6ZF6XJOHNPP2DMPAM4MW6OMBU \
  | 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: bfb25f5d2e3b5efd0d8f0338cb79cc0d3e3eed48d83d902a15919d0654f1eb1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c93d365807745b7dc333f3576e000e6618ff6d4002862a4d659b4a1b05eaea49",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2011-11-17T20:30:56Z",
    "title_canon_sha256": "fc0aa77b34525f98c04169204bdfafd203d127ff078012bfd7b4e6310e1fe7f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4201",
    "kind": "arxiv",
    "version": 1
  }
}