Pith Number

pith:4VEQAQ3W

pith:2010:4VEQAQ3WQKOS3CCJYMTAG77AQI

not attested not anchored not stored refs pending

Some applications of Frobenius algebras to Hopf algebras

Martin Lorenz

arxiv:1008.4054 v1 · 2010-08-24 · 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{4VEQAQ3WQKOS3CCJYMTAG77AQI}

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	2026-05-18T04:41:54.253235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e549004376829d2d8849c326037fe08235f68360eee8afd1787be431d45a943a

Aliases

arxiv: 1008.4054 · arxiv_version: 1008.4054v1 · doi: 10.48550/arxiv.1008.4054 · pith_short_12: 4VEQAQ3WQKOS · pith_short_16: 4VEQAQ3WQKOS3CCJ · pith_short_8: 4VEQAQ3W

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/4VEQAQ3WQKOS3CCJYMTAG77AQI \
  | 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: e549004376829d2d8849c326037fe08235f68360eee8afd1787be431d45a943a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "898d4085ff2911dae1af96df32e099087462d88c1df51dbd8d7863e37e2e34c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-08-24T14:19:02Z",
    "title_canon_sha256": "ab2d956769b6128c84d4bd5f8276cbe5eafc4e163f7318ca78e3763f9aec87a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4054",
    "kind": "arxiv",
    "version": 1
  }
}