Pith Number

pith:UQN3VGWN

pith:2012:UQN3VGWNPU3I4ELTFVJTLLHR3L

not attested not anchored not stored refs pending

Combinatorics of certain higher $q,t$-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula

Kyungyong Lee, Li Li, Nicholas A. Loehr

arxiv:1211.2191 v3 · 2012-11-09 · 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{UQN3VGWNPU3I4ELTFVJTLLHR3L}

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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	2026-07-05T00:16:01.103009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a41bba9acd7d368e11732d5335acf1dadcb5f29d629d17e0d5d2e2a392879781

Aliases

arxiv: 1211.2191 · arxiv_version: 1211.2191v3 · doi: 10.48550/arxiv.1211.2191 · pith_short_12: UQN3VGWNPU3I · pith_short_16: UQN3VGWNPU3I4ELT · pith_short_8: UQN3VGWN

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/UQN3VGWNPU3I4ELTFVJTLLHR3L \
  | 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: a41bba9acd7d368e11732d5335acf1dadcb5f29d629d17e0d5d2e2a392879781

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6d3448bf0f7db535ef8b6bb6fcfe202ec4ec6ea15f8f657af09e70e277c00a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-09T17:25:03Z",
    "title_canon_sha256": "cf980ee8d3c995290b89186971b2fe424862639ffe50f6384e313f738b540b0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2191",
    "kind": "arxiv",
    "version": 3
  }
}