Pith Number

pith:SUDBO63E

pith:2016:SUDBO63ENISNQJLRFB4HN535J7

not attested not anchored not stored refs pending

Catalan triangle numbers and binomial coefficients

Kyu-Hwan Lee, Se-Jin Oh

arxiv:1601.06685 v2 · 2016-01-25 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SUDBO63ENISNQJLRFB4HN535J7}

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	2026-05-18T00:32:44.719407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9506177b646a24d82571287876f77d4ff9705ba0ec90ab99eef58e8e17182bbd

Aliases

arxiv: 1601.06685 · arxiv_version: 1601.06685v2 · doi: 10.48550/arxiv.1601.06685 · pith_short_12: SUDBO63ENISN · pith_short_16: SUDBO63ENISNQJLR · pith_short_8: SUDBO63E

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/SUDBO63ENISNQJLRFB4HN535J7 \
  | 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: 9506177b646a24d82571287876f77d4ff9705ba0ec90ab99eef58e8e17182bbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1a7d163d9b1ba5185cc804ab083720a68e4b139317aaba0446f08be5eb588f2",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-25T17:21:50Z",
    "title_canon_sha256": "428a7307a79b4a0bef8bb610ec6e2aab3de1999aaeaf5250f5d4272ab8921573"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.06685",
    "kind": "arxiv",
    "version": 2
  }
}