Pith Number

pith:4CLYBIIX

pith:2015:4CLYBIIXKSY4UGJWWKMBM7L7FU

not attested not anchored not stored refs pending

A New Proof of $\bf{Z_{Kup}=|Z_{Henn}|^2}$ for Semisimple Hopf Algebras

Liang Chang

arxiv:1504.00743 v3 · 2015-04-03 · math.QA · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4CLYBIIXKSY4UGJWWKMBM7L7FU}

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	2026-05-18T01:13:28.709459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e09780a11754b1ca1936b298167d7f2d3a7d584fccf75b00fad6ad7105e10296

Aliases

arxiv: 1504.00743 · arxiv_version: 1504.00743v3 · doi: 10.48550/arxiv.1504.00743 · pith_short_12: 4CLYBIIXKSY4 · pith_short_16: 4CLYBIIXKSY4UGJW · pith_short_8: 4CLYBIIX

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/4CLYBIIXKSY4UGJWWKMBM7L7FU \
  | 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: e09780a11754b1ca1936b298167d7f2d3a7d584fccf75b00fad6ad7105e10296

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67ee1d88b4d9e2aecddd6f0a0778cc836655b9da535a34bf40610838565f4eed",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-04-03T04:58:32Z",
    "title_canon_sha256": "b82142560b8120ced4ce5a1d4581763a48068c05d911230f38b535da8fdc231a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00743",
    "kind": "arxiv",
    "version": 3
  }
}