Pith Number

pith:MK7GDZD2

pith:2005:MK7GDZD2FJUQM6P7VVR6L4FRZB

not attested not anchored not stored refs pending

The variance of the Stirling cycle numbers

Herbert S. Wilf

arxiv:math/0511428 v2 · 2005-11-17 · 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{MK7GDZD2FJUQM6P7VVR6L4FRZB}

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	2026-07-04T14:51:42.648893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62be61e47a2a690679ffad63e5f0b1c86e202c2de2010900a1fba9ee2cc72c8d

Aliases

arxiv: math/0511428 · arxiv_version: math/0511428v2 · doi: 10.48550/arxiv.math/0511428 · pith_short_12: MK7GDZD2FJUQ · pith_short_16: MK7GDZD2FJUQM6P7 · pith_short_8: MK7GDZD2

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/MK7GDZD2FJUQM6P7VVR6L4FRZB \
  | 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: 62be61e47a2a690679ffad63e5f0b1c86e202c2de2010900a1fba9ee2cc72c8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a004af5b4158b1753c5a25b27dccd8e12e2fcf861a6b5bd8cd460e58fa04891",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2005-11-17T02:55:41Z",
    "title_canon_sha256": "b88cc5d3fc7630c6245b84dd8b419db85c0af8fe0f9768dd3a6d5a751dc9cf73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0511428",
    "kind": "arxiv",
    "version": 2
  }
}