Pith Number

pith:4HQQYKWM

pith:2015:4HQQYKWMR75SEBWKKKPRDIYUPX

not attested not anchored not stored refs pending

Kibble-Slepian Formula and Generating Functions for 2$D$ Polynomials

Mourad E. H. Ismail, Ruiming Zhang

arxiv:1508.01816 v2 · 2015-08-01 · 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{4HQQYKWMR75SEBWKKKPRDIYUPX}

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	2026-05-18T01:15:23.369778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1e10c2acc8ffb2206ca529f11a3147dd8a81e17a29139034d5b4061496c8ddd

Aliases

arxiv: 1508.01816 · arxiv_version: 1508.01816v2 · doi: 10.48550/arxiv.1508.01816 · pith_short_12: 4HQQYKWMR75S · pith_short_16: 4HQQYKWMR75SEBWK · pith_short_8: 4HQQYKWM

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/4HQQYKWMR75SEBWKKKPRDIYUPX \
  | 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: e1e10c2acc8ffb2206ca529f11a3147dd8a81e17a29139034d5b4061496c8ddd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa092d3c91ec6c5da1ed0a2c85ab3709297fe684a885c68637733b2141971dfb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-01T02:25:22Z",
    "title_canon_sha256": "4ce44dcbf245dbf0bbda6bf101e49cc75f6e696d05a3a8300c57690722e205bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01816",
    "kind": "arxiv",
    "version": 2
  }
}