Pith Number

pith:77T5U6GW

pith:2013:77T5U6GWEHRP6LP6ZRD5E4PAPX

not attested not anchored not stored refs pending

Combinatorially interpreting generalized Stirling numbers

David Galvin, John Engbers, Justin Hilyard

arxiv:1308.2666 v5 · 2013-08-12 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{77T5U6GWEHRP6LP6ZRD5E4PAPX}

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	2026-05-18T02:47:05.717144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffe7da78d621e2ff2dfecc47d271e07de74a6eac5db5279d63b073f9e8b0e366

Aliases

arxiv: 1308.2666 · arxiv_version: 1308.2666v5 · doi: 10.48550/arxiv.1308.2666 · pith_short_12: 77T5U6GWEHRP · pith_short_16: 77T5U6GWEHRP6LP6 · pith_short_8: 77T5U6GW

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/77T5U6GWEHRP6LP6ZRD5E4PAPX \
  | 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: ffe7da78d621e2ff2dfecc47d271e07de74a6eac5db5279d63b073f9e8b0e366

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3ced13da54505b3b5d950d0b19a2803bd2ecfa5a05d537c031e8ad35d345302",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-08-12T19:58:26Z",
    "title_canon_sha256": "df3756a6f038d0084f5df90405147dc0140c95cd4bc03ee6e7d204f8ee6b0a0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2666",
    "kind": "arxiv",
    "version": 5
  }
}