Pith Number

pith:UMTI5UCN

pith:2004:UMTI5UCNI2DBGZYVUOBIWENNMH

not attested not anchored not stored refs pending

Congruences for Catalan and Motzkin numbers and related sequences

Bruce E. Sagan (Michigan State U.), Emeric Deutsch (Polytechnic U.)

arxiv:math/0407326 v1 · 2004-07-19 · 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{UMTI5UCNI2DBGZYVUOBIWENNMH}

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.

Cited by

1 paper in Pith

Factoring Catalan numbers

Receipt and verification

First computed	2026-07-04T14:38:56.189465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3268ed04d4686136715a3828b11ad61ca6b9b6afc9d5cb8aba41b8fa44202fa

Aliases

arxiv: math/0407326 · arxiv_version: math/0407326v1 · doi: 10.48550/arxiv.math/0407326 · pith_short_12: UMTI5UCNI2DB · pith_short_16: UMTI5UCNI2DBGZYV · pith_short_8: UMTI5UCN

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/UMTI5UCNI2DBGZYVUOBIWENNMH \
  | 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: a3268ed04d4686136715a3828b11ad61ca6b9b6afc9d5cb8aba41b8fa44202fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ee47123ede52358173de3d0a0f0146ab222f29c719fd3f44d5d70082fc33caf",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2004-07-19T16:23:28Z",
    "title_canon_sha256": "79c63ed1b475577aec11235296e0fce3635251aa41c1741887ab24e5f166a3f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407326",
    "kind": "arxiv",
    "version": 1
  }
}