Pith Number

pith:V2CGYKAT

pith:2010:V2CGYKATJXGHTQ66LLBZF6KOFU

not attested not anchored not stored refs pending

The odd Catalan numbers modulo 2^k

Hsueh-Yung Lin

arxiv:1012.1756 v2 · 2010-12-08 · math.NT · 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{V2CGYKATJXGHTQ66LLBZF6KOFU}

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	2026-05-18T04:31:50.992577Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae846c28134dcc79c3de5ac392f94e2d017b9b3ccab1754238badb2dfacf9c09

Aliases

arxiv: 1012.1756 · arxiv_version: 1012.1756v2 · doi: 10.48550/arxiv.1012.1756 · pith_short_12: V2CGYKATJXGH · pith_short_16: V2CGYKATJXGHTQ66 · pith_short_8: V2CGYKAT

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/V2CGYKATJXGHTQ66LLBZF6KOFU \
  | 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: ae846c28134dcc79c3de5ac392f94e2d017b9b3ccab1754238badb2dfacf9c09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3f5006ee77dad63900d592adc6d9286d3a17ff5b9dacbda24c9e419a988bcc4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-08T13:12:45Z",
    "title_canon_sha256": "4f1ffc8f32288d025873662d1de9cfd42cff5c502e429b5db1ababafc705612d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1756",
    "kind": "arxiv",
    "version": 2
  }
}