Pith Number

pith:TXMF7J2L

pith:2022:TXMF7J2LNDKI2PWKN4YA7GQWY5

not attested not anchored not stored refs pending

A combinatorial proof of a symmetry for a refinement of the Narayana numbers

Andr\'es R. Vindas-Mel\'endez, Gilbert Labelle, Joseph Pappe, Mikl\'os B\'ona, Stoyan Dimitrov, Yan Zhuang, Yifei Li

arxiv:2212.10586 v2 · 2022-12-20 · 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{TXMF7J2LNDKI2PWKN4YA7GQWY5}

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	2026-07-05T10:57:51.605601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dd85fa74b68d48d3eca6f300f9a16c74894206009ea8c611598d7bb57f1c4bb

Aliases

arxiv: 2212.10586 · arxiv_version: 2212.10586v2 · doi: 10.48550/arxiv.2212.10586 · pith_short_12: TXMF7J2LNDKI · pith_short_16: TXMF7J2LNDKI2PWK · pith_short_8: TXMF7J2L

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/TXMF7J2LNDKI2PWKN4YA7GQWY5 \
  | 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: 9dd85fa74b68d48d3eca6f300f9a16c74894206009ea8c611598d7bb57f1c4bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce5f3f0075dd7978378e0394decc1cff71ebfa9be36823491868ef44b80b089d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-12-20T19:01:01Z",
    "title_canon_sha256": "6ba86e8ab986bf636cb7be6a007591f1a1997e422c96d874e8db303f2a060c56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.10586",
    "kind": "arxiv",
    "version": 2
  }
}