Pith Number

pith:O5LHSKOW

pith:2004:O5LHSKOWBQA4MN74SNFZ2L4CZZ

not attested not anchored not stored refs pending

Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials

Paul Terwilliger

arxiv:math/0408390 v3 · 2004-08-27 · math.QA · 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{O5LHSKOWBQA4MN74SNFZ2L4CZZ}

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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

2 papers in Pith

Circular Hessenberg pairs and the tridiagonal relations

Leonard pairs, spin models, and distance-regular graphs

Receipt and verification

First computed	2026-07-04T15:10:56.100332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77567929d60c01c637fc934b9d2f82ce4544e7b31f3214b4295b872a53533e19

Aliases

arxiv: math/0408390 · arxiv_version: math/0408390v3 · doi: 10.48550/arxiv.math/0408390 · pith_short_12: O5LHSKOWBQA4 · pith_short_16: O5LHSKOWBQA4MN74 · pith_short_8: O5LHSKOW

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/O5LHSKOWBQA4MN74SNFZ2L4CZZ \
  | 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: 77567929d60c01c637fc934b9d2f82ce4544e7b31f3214b4295b872a53533e19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5953869453d9d394d64403a523ead542a0e248224d7ffa3798eb2f87b25ad625",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2004-08-27T20:39:17Z",
    "title_canon_sha256": "022584c0ae3d86d23e7540a78502f33140be6e3a000ba164aa39b1a1f55e3bbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0408390",
    "kind": "arxiv",
    "version": 3
  }
}