Pith Number

pith:64YSQCG4

pith:2019:64YSQCG4KKF2D4LMF7B4XFRZOD

not attested not anchored not stored refs pending

Arithmetic of weighted Catalan numbers

Andrew Gu, Yibo Gao

arxiv:1908.03914 v1 · 2019-08-11 · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{64YSQCG4KKF2D4LMF7B4XFRZOD}

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	2026-07-04T23:53:19.344407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7312808dc528ba1f16c2fc3cb963970ca16946f500bc8dfb04c97eccdde5777

Aliases

arxiv: 1908.03914 · arxiv_version: 1908.03914v1 · doi: 10.48550/arxiv.1908.03914 · pith_short_12: 64YSQCG4KKF2 · pith_short_16: 64YSQCG4KKF2D4LM · pith_short_8: 64YSQCG4

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/64YSQCG4KKF2D4LMF7B4XFRZOD \
  | 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: f7312808dc528ba1f16c2fc3cb963970ca16946f500bc8dfb04c97eccdde5777

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e814ff3bea00c4cfd73e8874e73d20c7f6ea44c821deddcc61d280b9f45667e",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-11T14:30:48Z",
    "title_canon_sha256": "54fd22d1a0ef716e8f10d9a0993b1b5d3e29eeeded060cdad12e9cab1825bde8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03914",
    "kind": "arxiv",
    "version": 1
  }
}