Pith Number

pith:AKWXRP73

pith:2012:AKWXRP73OP6DOR5HDUSREUB5GJ

not attested not anchored not stored refs pending

Krawtchouk polynomials, the Lie algebra $\mathfrak{sl}_2$, and Leonard pairs

Kazumasa Nomura, Paul Terwilliger

arxiv:1201.1645 v1 · 2012-01-08 · math.RT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AKWXRP73OP6DOR5HDUSREUB5GJ}

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	2026-05-18T04:05:02.904062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02ad78bffb73fc3747a71d2512503d325ade3f3baec051282872e6b31972058d

Aliases

arxiv: 1201.1645 · arxiv_version: 1201.1645v1 · doi: 10.48550/arxiv.1201.1645 · pith_short_12: AKWXRP73OP6D · pith_short_16: AKWXRP73OP6DOR5H · pith_short_8: AKWXRP73

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/AKWXRP73OP6DOR5HDUSREUB5GJ \
  | 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: 02ad78bffb73fc3747a71d2512503d325ade3f3baec051282872e6b31972058d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1713a6b6b0e7ef55816575ec44c539b964e95db1ca13daf99e77668badc90c99",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-01-08T17:55:37Z",
    "title_canon_sha256": "6f4317574637fab8fa5c4c7d6501523de5a870aa02a784f7b5de24ea1571f43e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.1645",
    "kind": "arxiv",
    "version": 1
  }
}