Pith Number

pith:MXSWBWFP

pith:2012:MXSWBWFPYFO44KOFZYUWDE4F4M

not attested not anchored not stored refs pending

Bessel polynomials, double factorials and context-free grammars

Shi-Mei Ma

arxiv:1208.5409 v3 · 2012-08-27 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MXSWBWFPYFO44KOFZYUWDE4F4M}

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	2026-05-18T03:46:30.401930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65e560d8afc15dce29c5ce29619385e30e1ea99cec693612f8187146ee73b091

Aliases

arxiv: 1208.5409 · arxiv_version: 1208.5409v3 · doi: 10.48550/arxiv.1208.5409 · pith_short_12: MXSWBWFPYFO4 · pith_short_16: MXSWBWFPYFO44KOF · pith_short_8: MXSWBWFP

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/MXSWBWFPYFO44KOFZYUWDE4F4M \
  | 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: 65e560d8afc15dce29c5ce29619385e30e1ea99cec693612f8187146ee73b091

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2af7bd2f4670fd28e5fadad2b54c7e8e8fd751627af36b74012b5337eee21120",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-27T14:34:42Z",
    "title_canon_sha256": "c3966d570132c7f022cfcbf9b0f093024f78fdf2c26a9e467dcee7daad2168fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5409",
    "kind": "arxiv",
    "version": 3
  }
}