Pith Number

pith:MCMBII47

pith:2013:MCMBII47XHUDDFLHVO5NJWLBNE

not attested not anchored not stored refs pending

Asymptotics of Chebyshev-Stirling and Stirling numbers of the second kind

Lance L. Littlejohn, Thorsten Neuschel, Wolfgang Gawronski

arxiv:1308.6803 v1 · 2013-08-30 · math.CO · 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{MCMBII47XHUDDFLHVO5NJWLBNE}

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	2026-05-18T03:14:30.868218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

609814239fb9e8319567abbad4d9616913192a0c481f8997f6bc35a8d09f1f52

Aliases

arxiv: 1308.6803 · arxiv_version: 1308.6803v1 · doi: 10.48550/arxiv.1308.6803 · pith_short_12: MCMBII47XHUD · pith_short_16: MCMBII47XHUDDFLH · pith_short_8: MCMBII47

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/MCMBII47XHUDDFLHVO5NJWLBNE \
  | 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: 609814239fb9e8319567abbad4d9616913192a0c481f8997f6bc35a8d09f1f52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "264712519f3fce063d92ec6f1233083fb87adefbd23dc84a88ce0c9aefeceeb6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-08-30T17:25:16Z",
    "title_canon_sha256": "a4f912e6a7369150e49aac42ee64bced65eb439c866eba637fc9ca8df8677633"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.6803",
    "kind": "arxiv",
    "version": 1
  }
}