Pith Number

pith:4DYFSMZZ

pith:2013:4DYFSMZZRU76JDTDGC7BMFIQMK

not attested not anchored not stored refs pending

The multivariate Krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states

Alexei Zhedanov, Luc Vinet, Vincent X. Genest

arxiv:1306.4256 v3 · 2013-06-18 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4DYFSMZZRU76JDTDGC7BMFIQMK}

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	2026-05-18T01:49:15.491410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0f05933398d3fe48e6330be16151062837ecb53d6b005f55862492340e97a5e

Aliases

arxiv: 1306.4256 · arxiv_version: 1306.4256v3 · doi: 10.48550/arxiv.1306.4256 · pith_short_12: 4DYFSMZZRU76 · pith_short_16: 4DYFSMZZRU76JDTD · pith_short_8: 4DYFSMZZ

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/4DYFSMZZRU76JDTDGC7BMFIQMK \
  | 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: e0f05933398d3fe48e6330be16151062837ecb53d6b005f55862492340e97a5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "338c6dfbdf71bac66ad606fbd7d2f1f5a9c1d3ba1c5e7b73bc409b81b7cd3ed7",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-06-18T16:04:12Z",
    "title_canon_sha256": "160a8e77cdfee9c258fb3c2b0ba4d8395b3c536e723cfb5754c8be45e53d837a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.4256",
    "kind": "arxiv",
    "version": 3
  }
}