Pith Number

pith:4ZRD5FCS

pith:2023:4ZRD5FCSPWDNCPTGGGZG4GKIOV

not attested not anchored not stored refs pending

Multivariate P- and/or Q-polynomial association schemes

Da Zhao, Eiichi Bannai, Hirotake Kurihara, Yan Zhu

arxiv:2305.00707 v2 · 2023-05-01 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ZRD5FCSPWDNCPTGGGZG4GKIOV}

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	2026-07-05T06:41:49.010775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6623e94527d86d13e6631b26e1948754b34a81e53b75d0ba1d79fc7de7721e6

Aliases

arxiv: 2305.00707 · arxiv_version: 2305.00707v2 · doi: 10.48550/arxiv.2305.00707 · pith_short_12: 4ZRD5FCSPWDN · pith_short_16: 4ZRD5FCSPWDNCPTG · pith_short_8: 4ZRD5FCS

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/4ZRD5FCSPWDNCPTGGGZG4GKIOV \
  | 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: e6623e94527d86d13e6631b26e1948754b34a81e53b75d0ba1d79fc7de7721e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0483fcfc5cbd36796fa49d042a0a9e4737d234649198840bc46f6ef3675899d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-05-01T08:12:00Z",
    "title_canon_sha256": "ef2f828e74ae42f1c84b7c5b6cbd4e0df0f6a52c26eede8b6a2b09e3da15cef3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2305.00707",
    "kind": "arxiv",
    "version": 2
  }
}