Pith Number

pith:66XCOTVE

pith:2015:66XCOTVEZXRCLC5GMRO7S2RSDX

not attested not anchored not stored refs pending

Generalized Catalan Numbers and the Enumeration of Planar Embeddings

Jonathan E. Beagley, Paul Drube

arxiv:1501.07137 v1 · 2015-01-28 · 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{66XCOTVEZXRCLC5GMRO7S2RSDX}

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	2026-05-18T02:28:30.121775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7ae274ea4cde2258ba6645df96a321df2f32d33d97d80da3c3fa5b2374dcef6

Aliases

arxiv: 1501.07137 · arxiv_version: 1501.07137v1 · doi: 10.48550/arxiv.1501.07137 · pith_short_12: 66XCOTVEZXRC · pith_short_16: 66XCOTVEZXRCLC5G · pith_short_8: 66XCOTVE

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/66XCOTVEZXRCLC5GMRO7S2RSDX \
  | 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: f7ae274ea4cde2258ba6645df96a321df2f32d33d97d80da3c3fa5b2374dcef6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09a56d43d04da758fae1b5ff17dafba508adcf091ffe71ddb63c56205072a04d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-28T15:13:42Z",
    "title_canon_sha256": "b2605762a1bf6c2ecd464ef0d9d30207a9ae4f5d3baba649e69dfd40db747553"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.07137",
    "kind": "arxiv",
    "version": 1
  }
}