Pith Number

pith:N425PND5

pith:2016:N425PND5S5QFMPHWVJBETAGLUQ

not attested not anchored not stored refs pending

Motzkin numbers and related sequences modulo powers of $2$

Christian Krattenthaler (Universit\"at Wien), Thomas W. M\"uller (Queen Mary & Westfield College, University of London)

arxiv:1608.05657 v3 · 2016-08-19 · 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{N425PND5S5QFMPHWVJBETAGLUQ}

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	2026-05-18T00:12:35.700805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f35d7b47d9760563cf6aa424980cba4245c71a49e6e426f47077774d6efe7b4

Aliases

arxiv: 1608.05657 · arxiv_version: 1608.05657v3 · doi: 10.48550/arxiv.1608.05657 · pith_short_12: N425PND5S5QF · pith_short_16: N425PND5S5QFMPHW · pith_short_8: N425PND5

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/N425PND5S5QFMPHWVJBETAGLUQ \
  | 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: 6f35d7b47d9760563cf6aa424980cba4245c71a49e6e426f47077774d6efe7b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f231979f99a5b2fdc8ef22657504237a638db7d3177807bab517988d1a59386",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-19T16:27:45Z",
    "title_canon_sha256": "8952e50aebb534087bdfe4689f1e82fed3749c4ff62dae3ff7a575a5ba8d9558"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05657",
    "kind": "arxiv",
    "version": 3
  }
}