Pith Number

pith:K3TCMURX

pith:2009:K3TCMURXEELDBBBZTTRCGRB4V5

not attested not anchored not stored refs pending

Square Partitions and Catalan Numbers

Matthew Bennett, Nathan Manning, R.J. Dolbin, Vyjayanthi Chari

arxiv:0912.4983 v1 · 2009-12-25 · math.RT · 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{K3TCMURXEELDBBBZTTRCGRB4V5}

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	2026-05-18T03:48:46.754208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56e626523721163084399ce223443caf66a2359fcfe24e4091de5a2008a121f1

Aliases

arxiv: 0912.4983 · arxiv_version: 0912.4983v1 · doi: 10.48550/arxiv.0912.4983 · pith_short_12: K3TCMURXEELD · pith_short_16: K3TCMURXEELDBBBZ · pith_short_8: K3TCMURX

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/K3TCMURXEELDBBBZTTRCGRB4V5 \
  | 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: 56e626523721163084399ce223443caf66a2359fcfe24e4091de5a2008a121f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "444b9e50fac86a3b6a4ac177c1f77ecec8baaeffa70ccc1c34f5abf4370a5a2c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2009-12-25T20:52:35Z",
    "title_canon_sha256": "db5acccb8588ddd43018c3db0b95406b97a0327260e4738ee8defd9fd4176310"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.4983",
    "kind": "arxiv",
    "version": 1
  }
}