Pith Number

pith:43B345Z5

pith:2015:43B345Z55RYX54A4DVLURQRPLQ

not attested not anchored not stored refs pending

Central binomial coefficients also count (2431,4231,1432,4132)-avoiders

Marie-Louise Bruner

arxiv:1505.04929 v2 · 2015-05-19 · 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{43B345Z55RYX54A4DVLURQRPLQ}

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	2026-05-18T02:00:01.926456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6c3be773dec717ef01c1d5748c22f5c20f1367aa9203fa09a395d06cadb7556

Aliases

arxiv: 1505.04929 · arxiv_version: 1505.04929v2 · doi: 10.48550/arxiv.1505.04929 · pith_short_12: 43B345Z55RYX · pith_short_16: 43B345Z55RYX54A4 · pith_short_8: 43B345Z5

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/43B345Z55RYX54A4DVLURQRPLQ \
  | 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: e6c3be773dec717ef01c1d5748c22f5c20f1367aa9203fa09a395d06cadb7556

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88ca56abfa3dbeeb0f0e3b3d16760a28a974cc8bcac4a482300a5289d8cede07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-19T09:42:37Z",
    "title_canon_sha256": "1fe92bb5df9dae9bc7437ccdb0e40e928fe4b28518a4f3ac10a8fb34ff57d26e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04929",
    "kind": "arxiv",
    "version": 2
  }
}