Pith Number

pith:O4RSL2BV

pith:2025:O4RSL2BVD2P7YFR4RSTGRMNBTI

not attested not anchored not stored refs pending

A class of (infinite-dimensional) cosemisimple Hopf algebras constructed via abelian extensions

Gongxiang Liu, Jing Yu, Kun Zhou, Xiangjun Zhen

arxiv:2506.04008 v1 · 2025-06-04 · math.QA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O4RSL2BVD2P7YFR4RSTGRMNBTI}

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	2026-07-05T11:15:55.230336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

772325e8351e9ffc163c8ca668b1a19a118a44b50ac9bd2373db33312d33d439

Aliases

arxiv: 2506.04008 · arxiv_version: 2506.04008v1 · doi: 10.48550/arxiv.2506.04008 · pith_short_12: O4RSL2BVD2P7 · pith_short_16: O4RSL2BVD2P7YFR4 · pith_short_8: O4RSL2BV

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/O4RSL2BVD2P7YFR4RSTGRMNBTI \
  | 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: 772325e8351e9ffc163c8ca668b1a19a118a44b50ac9bd2373db33312d33d439

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9caa590cf0f02802276995f0977519d27e5790c7e123038546db596f566f8260",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2025-06-04T14:34:54Z",
    "title_canon_sha256": "3c22c2b1c20d7ee53332f315946761b69feccd2322eefd8ea4a827e3a9724325"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.04008",
    "kind": "arxiv",
    "version": 1
  }
}