Pith Number

pith:NPQNWMVZ

pith:2011:NPQNWMVZIBSE6WJMVV5F2AHLRT

not attested not anchored not stored refs pending

The Jacobi-Stirling Numbers

Eric S. Egge, George E. Andrews, Lance L. Littlejohn, Wolfgang Gawronski

arxiv:1112.6111 v1 · 2011-12-28 · 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{NPQNWMVZIBSE6WJMVV5F2AHLRT}

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	2026-05-18T04:05:36.760181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6be0db32b940644f592cad7a5d00eb8cfc84bab793ed259d0854227d97ab306e

Aliases

arxiv: 1112.6111 · arxiv_version: 1112.6111v1 · doi: 10.48550/arxiv.1112.6111 · pith_short_12: NPQNWMVZIBSE · pith_short_16: NPQNWMVZIBSE6WJM · pith_short_8: NPQNWMVZ

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/NPQNWMVZIBSE6WJMVV5F2AHLRT \
  | 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: 6be0db32b940644f592cad7a5d00eb8cfc84bab793ed259d0854227d97ab306e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "608ac3047fc60d7599241055fb8378a4e92854e6ca935a3609c261c5931db6fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-28T12:53:24Z",
    "title_canon_sha256": "ee113ee06de33c87aaebd4672d077f1b52776d7f1622e13908819c73f79f8d74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6111",
    "kind": "arxiv",
    "version": 1
  }
}