Pith Number

pith:UWO3BJBC

pith:2015:UWO3BJBCEKI3CSPK6FWOFPALIP

not attested not anchored not stored refs pending

Congruences involving Franel and Catalan-Larcombe-French numbers

Zhi-Hong Sun

arxiv:1502.02499 v3 · 2015-02-09 · math.NT · 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{UWO3BJBCEKI3CSPK6FWOFPALIP}

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	2026-05-18T02:17:11.209649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a59db0a4222291b149eaf16ce2bc0b43ec01bdc430c9f611e9d4c31f1a3697b2

Aliases

arxiv: 1502.02499 · arxiv_version: 1502.02499v3 · doi: 10.48550/arxiv.1502.02499 · pith_short_12: UWO3BJBCEKI3 · pith_short_16: UWO3BJBCEKI3CSPK · pith_short_8: UWO3BJBC

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/UWO3BJBCEKI3CSPK6FWOFPALIP \
  | 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: a59db0a4222291b149eaf16ce2bc0b43ec01bdc430c9f611e9d4c31f1a3697b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ee99196c6410b4097cdfaf98ace1bdb342846009e3a7568d4757cf419ec721b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-02-09T14:33:30Z",
    "title_canon_sha256": "762e2023a86c25baf6a005a6d915aeac29738653117454eeef29553618625c51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02499",
    "kind": "arxiv",
    "version": 3
  }
}