Pith Number

pith:QELLJEKI

pith:2013:QELLJEKIGAQV2TNOVGMXUER3WH

not attested not anchored not stored refs pending

A determinant representation for generalized ballot and Fuss-Catalan numbers

James J.Y. Zhao

arxiv:1312.3164 v1 · 2013-12-11 · 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{QELLJEKIGAQV2TNOVGMXUER3WH}

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	2026-05-18T03:05:00.326595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8116b4914830215d4daea9997a123bb1c8c8e3d992711d62ce11dc1ed0ef57dd

Aliases

arxiv: 1312.3164 · arxiv_version: 1312.3164v1 · doi: 10.48550/arxiv.1312.3164 · pith_short_12: QELLJEKIGAQV · pith_short_16: QELLJEKIGAQV2TNO · pith_short_8: QELLJEKI

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/QELLJEKIGAQV2TNOVGMXUER3WH \
  | 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: 8116b4914830215d4daea9997a123bb1c8c8e3d992711d62ce11dc1ed0ef57dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71fc0852b1746fec5b9850024f962c3a2d4aa0d5cd0ddb3804d72ff14b3e2bf8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-11T13:52:10Z",
    "title_canon_sha256": "5c31c01a00adb763a8399cf8d31dbfa626b06c233edc2b881b58999720f97d6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3164",
    "kind": "arxiv",
    "version": 1
  }
}