Pith Number

pith:WTOSKOLQ

pith:2021:WTOSKOLQXA6ZSCFHZNRUIBFFLM

not attested not anchored not stored refs pending

Multi-Lah numbers and multi-Stirling numbers of the first kind

Dae San Kim, Hye Kyun Kim, Hyunseok Lee, Seongho Park, Taekyun Kim

arxiv:2106.10917 v1 · 2021-06-21 · 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{WTOSKOLQXA6ZSCFHZNRUIBFFLM}

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	2026-07-05T02:50:54.623124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4dd253970b83d9908a7cb634404a55b337734f0f953dc8b22def02fe29531e9

Aliases

arxiv: 2106.10917 · arxiv_version: 2106.10917v1 · doi: 10.48550/arxiv.2106.10917 · pith_short_12: WTOSKOLQXA6Z · pith_short_16: WTOSKOLQXA6ZSCFH · pith_short_8: WTOSKOLQ

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/WTOSKOLQXA6ZSCFHZNRUIBFFLM \
  | 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: b4dd253970b83d9908a7cb634404a55b337734f0f953dc8b22def02fe29531e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "043680f69dc5ef0e523ccb9528bb8b78e17a8d97d6b036f66ec93f0dc7989b28",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-06-21T08:33:58Z",
    "title_canon_sha256": "e43722fa3b9b41a87ec7354e5a4335d648afeb22591ff122c96150868d16ec69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.10917",
    "kind": "arxiv",
    "version": 1
  }
}