Pith Number

pith:4GN5BGSX

pith:2015:4GN5BGSXVMOLKQ7I7XWK6ZBHOQ

not attested not anchored not stored refs pending

Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers

Istv\'an Mez\H{o}, Kalman Liptai, Takao Komatsu

arxiv:1510.05799 v2 · 2015-10-20 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4GN5BGSXVMOLKQ7I7XWK6ZBHOQ}

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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.

Cited by

2 papers in Pith

The Bottleneck Birthday Problem

Partial degenerate Stirling numbers

Receipt and verification

First computed	2026-05-18T01:29:23.187150Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e19bd09a57ab1cb543e8fdecaf64277405e0ae02f7760c0287a1d1ffe2216d62

Aliases

arxiv: 1510.05799 · arxiv_version: 1510.05799v2 · doi: 10.48550/arxiv.1510.05799 · pith_short_12: 4GN5BGSXVMOL · pith_short_16: 4GN5BGSXVMOLKQ7I · pith_short_8: 4GN5BGSX

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/4GN5BGSXVMOLKQ7I7XWK6ZBHOQ \
  | 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: e19bd09a57ab1cb543e8fdecaf64277405e0ae02f7760c0287a1d1ffe2216d62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "154974622f59191f9b1269c95f49d13d2aa71fc84bd09b6346fc1346c96773db",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-20T09:10:30Z",
    "title_canon_sha256": "69046c256e0ab4bd142c4d31aa8bbea17bbb0934fdf4499c3b2681824e7135b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05799",
    "kind": "arxiv",
    "version": 2
  }
}