Pith Number

pith:SD5BIWAV

pith:2013:SD5BIWAVOW2RHSO476Q2G4COUV

not attested not anchored not stored refs pending

A curious polynomial interpolation of Carlitz-Riordan's $q$-ballot numbers

Fr\'ed\'eric Chapoton (ICJ), Jiang Zeng (ICJ)

arxiv:1311.7228 v2 · 2013-11-28 · 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{SD5BIWAVOW2RHSO476Q2G4COUV}

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	2026-05-18T03:04:24.798763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90fa14581575b513c9dcffa1a3704ea56e04dae8d1b43e9749292163bc50a15d

Aliases

arxiv: 1311.7228 · arxiv_version: 1311.7228v2 · doi: 10.48550/arxiv.1311.7228 · pith_short_12: SD5BIWAVOW2R · pith_short_16: SD5BIWAVOW2RHSO4 · pith_short_8: SD5BIWAV

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/SD5BIWAVOW2RHSO476Q2G4COUV \
  | 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: 90fa14581575b513c9dcffa1a3704ea56e04dae8d1b43e9749292163bc50a15d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b355cd96cd70cd6b38d50ede5fee0e586d55dcf9a96b5d479975c4ed6e9387d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-28T07:28:45Z",
    "title_canon_sha256": "5b14a321c2a258fb8166e2303beabc0bf8eeb88f228a8164fa88f9ec85b6756b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.7228",
    "kind": "arxiv",
    "version": 2
  }
}