Pith Number

pith:ZPZABGKI

pith:2018:ZPZABGKIB7A44OGCV2MMGDLDPR

not attested not anchored not stored refs pending

On Motzkin numbers and central trinomial coefficients

Zhi-Wei Sun

arxiv:1801.08905 v3 · 2018-01-26 · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZPZABGKIB7A44OGCV2MMGDLDPR}

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	2026-07-05T03:52:52.453798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbf20099480fc1ce38c2ae98c30d637c4280f8adba40573a457826c035954bc4

Aliases

arxiv: 1801.08905 · arxiv_version: 1801.08905v3 · doi: 10.48550/arxiv.1801.08905 · pith_short_12: ZPZABGKIB7A4 · pith_short_16: ZPZABGKIB7A44OGC · pith_short_8: ZPZABGKI

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/ZPZABGKIB7A44OGCV2MMGDLDPR \
  | 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: cbf20099480fc1ce38c2ae98c30d637c4280f8adba40573a457826c035954bc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa59612fb310e8d3d45f3a451c990bd53a0fe26bcc849233493977d4eccfdbfa",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-01-26T17:30:51Z",
    "title_canon_sha256": "f17c23bd9b4318b623a040cb69ece7af8617dab013cb47d602314951d93b6da2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.08905",
    "kind": "arxiv",
    "version": 3
  }
}