Pith Number

pith:DTKYO7HL

pith:2012:DTKYO7HLOZ73JUOLWXGPNYUZIV

not attested not anchored not stored refs pending

The Super Catalan Numbers $S(m, m + s)$ for $s \leq 4$

Jane Wang, Xin Chen

arxiv:1208.4196 v1 · 2012-08-21 · 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{DTKYO7HLOZ73JUOLWXGPNYUZIV}

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	2026-05-18T03:48:24.651519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cd5877ceb767fb4d1cbb5ccf6e29945774d7644479485ee84449e5603b81911

Aliases

arxiv: 1208.4196 · arxiv_version: 1208.4196v1 · doi: 10.48550/arxiv.1208.4196 · pith_short_12: DTKYO7HLOZ73 · pith_short_16: DTKYO7HLOZ73JUOL · pith_short_8: DTKYO7HL

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/DTKYO7HLOZ73JUOLWXGPNYUZIV \
  | 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: 1cd5877ceb767fb4d1cbb5ccf6e29945774d7644479485ee84449e5603b81911

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "385253b38140289f45c0acf121f3c40841bce4f4bc067f8bec8a936b449ff742",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-21T06:01:14Z",
    "title_canon_sha256": "47bcab1ac61096d753d6191b3461f311ac813ee31dc5298e44b3eb2219b72f45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4196",
    "kind": "arxiv",
    "version": 1
  }
}