Pith Number

pith:BWDEJ2GK

pith:1999:BWDEJ2GKDTHPNNBIJHV3KO63X5

not attested not anchored not stored refs pending

Differential equations for symmetric generalized ultraspherical polynomials

Roelof Koekoek

arxiv:math/9908143 v1 · 1999-08-27 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BWDEJ2GKDTHPNNBIJHV3KO63X5}

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	2026-07-04T14:41:17.362338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d8644e8ca1ccef6b42849ebb53bdbbf63dcbeba49b2a02708913e868a1d0e26

Aliases

arxiv: math/9908143 · arxiv_version: math/9908143v1 · doi: 10.48550/arxiv.math/9908143 · pith_short_12: BWDEJ2GKDTHP · pith_short_16: BWDEJ2GKDTHPNNBI · pith_short_8: BWDEJ2GK

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/BWDEJ2GKDTHPNNBIJHV3KO63X5 \
  | 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: 0d8644e8ca1ccef6b42849ebb53bdbbf63dcbeba49b2a02708913e868a1d0e26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92fdd8f34440fc8d71e1567e2c66e98a354fc1efde3afc60da7c3767df8cc77a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "1999-08-27T19:54:53Z",
    "title_canon_sha256": "12990674b4be720012020b4c66b7eabc0c984640bc9f5ef3a5d917d61adde407"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9908143",
    "kind": "arxiv",
    "version": 1
  }
}