Pith Number

pith:FXMO5DLV

pith:2015:FXMO5DLVWMQ67XY6QIPYR3GEJK

not attested not anchored not stored refs pending

Modular Catalan Numbers

Jia Huang, Nickolas Hein

arxiv:1508.01688 v5 · 2015-08-07 · 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{FXMO5DLVWMQ67XY6QIPYR3GEJK}

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	2026-05-18T00:59:35.542371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dd8ee8d75b321efdf1e821f88ecc44a85c71fa66cb94cccb4b17a0d51247f2e

Aliases

arxiv: 1508.01688 · arxiv_version: 1508.01688v5 · doi: 10.48550/arxiv.1508.01688 · pith_short_12: FXMO5DLVWMQ6 · pith_short_16: FXMO5DLVWMQ67XY6 · pith_short_8: FXMO5DLV

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/FXMO5DLVWMQ67XY6QIPYR3GEJK \
  | 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: 2dd8ee8d75b321efdf1e821f88ecc44a85c71fa66cb94cccb4b17a0d51247f2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "816efcec8342634d760e727a4073251adeea11c33e46b5c75ff37cbeed55c8fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-07T13:39:06Z",
    "title_canon_sha256": "dc87237ec54c57756367d58be79c84d5c2a492d531192a6d685d1cd426e91466"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01688",
    "kind": "arxiv",
    "version": 5
  }
}