Pith Number

pith:R45NDGHA

pith:2012:R45NDGHAL5G3A2UAPPAF66F747

not attested not anchored not stored refs pending

Spectral decomposition and matrix-valued orthogonal polynomials

Erik Koelink, Mourad E. H. Ismail, Wolter Groenevelt

arxiv:1206.4785 v1 · 2012-06-21 · math.CA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R45NDGHAL5G3A2UAPPAF66F747}

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	2026-05-18T02:56:35.546760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f3ad198e05f4db06a807bc05f78bfe7da627bb602348ba42888f8337975cd71

Aliases

arxiv: 1206.4785 · arxiv_version: 1206.4785v1 · doi: 10.48550/arxiv.1206.4785 · pith_short_12: R45NDGHAL5G3 · pith_short_16: R45NDGHAL5G3A2UA · pith_short_8: R45NDGHA

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/R45NDGHAL5G3A2UAPPAF66F747 \
  | 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: 8f3ad198e05f4db06a807bc05f78bfe7da627bb602348ba42888f8337975cd71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c020c1c3275cc7b133b0d3f022bac018ae6ded523cea168aa7f223cbdbb1189",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-06-21T06:48:55Z",
    "title_canon_sha256": "5eb14e2b9aa28b59f19d222d04a30ef94ca57d701927bd23648142aae4244a39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4785",
    "kind": "arxiv",
    "version": 1
  }
}