Pith Number

pith:4WJZBYR6

pith:2014:4WJZBYR67NMWJK77QDR4ZQROAT

not attested not anchored not stored refs pending

The $(m,n)$-rational $q, t$-Catalan polynomials for $m=3$ and their $q,t$-symmetry

Huilan Li, Ryan Kaliszewski

arxiv:1412.3475 v2 · 2014-12-10 · 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{4WJZBYR67NMWJK77QDR4ZQROAT}

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	2026-05-18T01:30:25.529257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e59390e23efb5964abff80e3ccc22e04c421f3824b3317b79b32ed71f9122fd0

Aliases

arxiv: 1412.3475 · arxiv_version: 1412.3475v2 · doi: 10.48550/arxiv.1412.3475 · pith_short_12: 4WJZBYR67NMW · pith_short_16: 4WJZBYR67NMWJK77 · pith_short_8: 4WJZBYR6

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/4WJZBYR67NMWJK77QDR4ZQROAT \
  | 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: e59390e23efb5964abff80e3ccc22e04c421f3824b3317b79b32ed71f9122fd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5c9d72c5b8c4331484efc2c47dfe5a7ba5a2ab9e0aa6f43596213e7f10134a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-12-10T21:20:59Z",
    "title_canon_sha256": "d49f3377fc0a6907a502a97d77021a335905f10c2c6b6e5448dc38e73d3b9d44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.3475",
    "kind": "arxiv",
    "version": 2
  }
}