Pith Number

pith:5MHDH7MN

pith:2015:5MHDH7MNF77RJZB4FJE6DS3Q6D

not attested not anchored not stored refs pending

On the (n,k)-th Catalan numbers

Dongseok Kim

arxiv:1501.06799 v1 · 2015-01-27 · 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{5MHDH7MNF77RJZB4FJE6DS3Q6D}

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	2026-05-18T02:28:32.593843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb0e33fd8d2fff14e43c2a49e1cb70f0d96a8dc904a909ee39a6128a3d7e868b

Aliases

arxiv: 1501.06799 · arxiv_version: 1501.06799v1 · doi: 10.48550/arxiv.1501.06799 · pith_short_12: 5MHDH7MNF77R · pith_short_16: 5MHDH7MNF77RJZB4 · pith_short_8: 5MHDH7MN

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/5MHDH7MNF77RJZB4FJE6DS3Q6D \
  | 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: eb0e33fd8d2fff14e43c2a49e1cb70f0d96a8dc904a909ee39a6128a3d7e868b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ed995bf03843c870abbd890ba9dddbb0ba239a456bd2170a896f389f8732568",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-27T15:49:30Z",
    "title_canon_sha256": "167dc89fc1aae7a445e791419b47665000d3843850a0ae46c8638261a8efa6fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.06799",
    "kind": "arxiv",
    "version": 1
  }
}