Pith Number

pith:75ET4O4Z

pith:2012:75ET4O4ZE3KYZQWXONNGEE6X2D

not attested not anchored not stored refs pending

Identities of Eulerain and ordered Stirling numbers over a multiset

Joon Yop Lee

arxiv:1209.1199 v1 · 2012-09-06 · 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{75ET4O4ZE3KYZQWXONNGEE6X2D}

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	2026-05-18T03:46:06.278727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff493e3b9926d58cc2d7735a6213d7d0faa7eaee722de6777e9a62d2515cf920

Aliases

arxiv: 1209.1199 · arxiv_version: 1209.1199v1 · doi: 10.48550/arxiv.1209.1199 · pith_short_12: 75ET4O4ZE3KY · pith_short_16: 75ET4O4ZE3KYZQWX · pith_short_8: 75ET4O4Z

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/75ET4O4ZE3KYZQWXONNGEE6X2D \
  | 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: ff493e3b9926d58cc2d7735a6213d7d0faa7eaee722de6777e9a62d2515cf920

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10aa2c436118a8bc8c39aaabb5224e10eb81966f03bf4086dfbb707043df97d5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-06T07:09:31Z",
    "title_canon_sha256": "0a037a7ed21cb41383d372e60d4f5bc1f4141e7bf520563270a70c9ec840408f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1199",
    "kind": "arxiv",
    "version": 1
  }
}