Pith Number

pith:WUTQYWXK

pith:2018:WUTQYWXKB2F7MCYVFHIYIH4LOM

not attested not anchored not stored refs pending

$(q,t)$-Catalan numbers: gamma expansions, pattern avoidance and the $(-1)$-phenomenon

Bin Han, Dazhao Tang, Jiang Zeng, Shishuo Fu

arxiv:1805.08945 v2 · 2018-05-23 · 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{WUTQYWXKB2F7MCYVFHIYIH4LOM}

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	2026-05-18T00:03:24.483865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5270c5aea0e8bf60b1529d1841f8b730c895f65d6bfe0bdad7623511e27f00c

Aliases

arxiv: 1805.08945 · arxiv_version: 1805.08945v2 · doi: 10.48550/arxiv.1805.08945 · pith_short_12: WUTQYWXKB2F7 · pith_short_16: WUTQYWXKB2F7MCYV · pith_short_8: WUTQYWXK

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/WUTQYWXKB2F7MCYVFHIYIH4LOM \
  | 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: b5270c5aea0e8bf60b1529d1841f8b730c895f65d6bfe0bdad7623511e27f00c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "754579676bd9745035c8aac97ad29ffcd66721c4cf67ba523e67afca1df05224",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-05-23T03:19:40Z",
    "title_canon_sha256": "03c16f67ddc61b58c289a9897b0a8f1a6fe48286db286b15cba3ba06bfa995fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.08945",
    "kind": "arxiv",
    "version": 2
  }
}