Pith Number

pith:N7BJQYGC

pith:2025:N7BJQYGCYCKHDQFOHLC4XKUAW6

not attested not anchored not stored refs pending

An identity relating Catalan numbers to tangent numbers with arithmetic applications

Tongyuan Zhao, Yongchun Zang, Zhicong Lin

arxiv:2507.20965 v2 · 2025-07-28 · 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{N7BJQYGCYCKHDQFOHLC4XKUAW6}

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	2026-07-05T11:52:22.410023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fc29860c2c09471c0ae3ac5cbaa80b786c771929b845e71822be771327ddf71

Aliases

arxiv: 2507.20965 · arxiv_version: 2507.20965v2 · doi: 10.48550/arxiv.2507.20965 · pith_short_12: N7BJQYGCYCKH · pith_short_16: N7BJQYGCYCKHDQFO · pith_short_8: N7BJQYGC

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/N7BJQYGCYCKHDQFOHLC4XKUAW6 \
  | 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: 6fc29860c2c09471c0ae3ac5cbaa80b786c771929b845e71822be771327ddf71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f00ee1e42b8138c29543cb9790a1d5697c25e72ed5920ab9fa0cc2fceb0b1b67",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-28T16:20:14Z",
    "title_canon_sha256": "2691ef6dbf156a8935c219d49f1b848481bfdad442b6183d3fa15b1385d66e69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20965",
    "kind": "arxiv",
    "version": 2
  }
}