Pith Number

pith:T7ZRQJ4Y

pith:2015:T7ZRQJ4YZ37BTIMBJYQHDXNCQT

not attested not anchored not stored refs pending

Frobenius Divisibility for Hopf Algebras

Adam Jacoby, Martin Lorenz

arxiv:1511.02130 v1 · 2015-11-06 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T7ZRQJ4YZ37BTIMBJYQHDXNCQT}

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	2026-05-18T01:27:37.694142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ff3182798cefe19a1814e2071dda284ffbe254ff22960e8e0c4ca24867ca8e9

Aliases

arxiv: 1511.02130 · arxiv_version: 1511.02130v1 · doi: 10.48550/arxiv.1511.02130 · pith_short_12: T7ZRQJ4YZ37B · pith_short_16: T7ZRQJ4YZ37BTIMB · pith_short_8: T7ZRQJ4Y

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/T7ZRQJ4YZ37BTIMBJYQHDXNCQT \
  | 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: 9ff3182798cefe19a1814e2071dda284ffbe254ff22960e8e0c4ca24867ca8e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bedb507f188aec15d15825e633c262298c72a3ca5d57e9c99b015ecc87300e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-11-06T15:59:49Z",
    "title_canon_sha256": "a19d5c8daf7fece727c8d9e330e78fd61da38314e85d7d001acf84caf0022a07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02130",
    "kind": "arxiv",
    "version": 1
  }
}