Pith Number

pith:4TZ4CWIE

pith:1999:4TZ4CWIEB552OOYEENX6ZECZYM

not attested not anchored not stored refs pending

Weak Hopf Algebras II: Representation theory, dimensions and the Markov trace

G. Bohm, K. Szlachanyi

arxiv:math/9906045 v1 · 1999-06-08 · 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{4TZ4CWIEB552OOYEENX6ZECZYM}

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.

Cited by

1 paper in Pith

Two-Dimensional Bialgebras and Quantum Groups: Algebraic Structures and Tensor Network Realizations

Receipt and verification

First computed	2026-07-04T14:41:11.118279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4f3c159040f7ba73b04236fec9059c330f7267c451b719ecbe13769f0cc47bb

Aliases

arxiv: math/9906045 · arxiv_version: math/9906045v1 · doi: 10.48550/arxiv.math/9906045 · pith_short_12: 4TZ4CWIEB552 · pith_short_16: 4TZ4CWIEB552OOYE · pith_short_8: 4TZ4CWIE

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/4TZ4CWIEB552OOYEENX6ZECZYM \
  | 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: e4f3c159040f7ba73b04236fec9059c330f7267c451b719ecbe13769f0cc47bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c67ffca2b4f673f90976e768b1e40facb68f623855e15db39df439b88477d43",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "1999-06-08T13:22:21Z",
    "title_canon_sha256": "6e944499758c26692fb029a7a5e80afa8dd977477ea51f4326a954bb438e09c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9906045",
    "kind": "arxiv",
    "version": 1
  }
}