Pith Number

pith:XDLCPBJB

pith:2025:XDLCPBJBZ7TMPDY33EIRH4V7RQ

not attested not anchored not stored refs pending

A study of a recursive sequence of polynomials revealing weighted Catalan Numbers

Elizabeth Mrema, Sophie Marques

arxiv:2501.13693 v1 · 2025-01-23 · 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{XDLCPBJBZ7TMPDY33EIRH4V7RQ}

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	2026-07-05T10:04:32.679151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8d6278521cfe6c78f1bd91113f2bf8c03239bf79c34ecd3d797fd125af1fa55

Aliases

arxiv: 2501.13693 · arxiv_version: 2501.13693v1 · doi: 10.48550/arxiv.2501.13693 · pith_short_12: XDLCPBJBZ7TM · pith_short_16: XDLCPBJBZ7TMPDY3 · pith_short_8: XDLCPBJB

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/XDLCPBJBZ7TMPDY33EIRH4V7RQ \
  | 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: b8d6278521cfe6c78f1bd91113f2bf8c03239bf79c34ecd3d797fd125af1fa55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5e21a0df1f4e805c82860266737c0fec0538b8e9c0f0aa1eed46c1c40960a02",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-01-23T14:17:16Z",
    "title_canon_sha256": "b5de58619655588643cd82bfc70f0d5bf0a94e38abdf5e70d0dcb85fb4670f7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.13693",
    "kind": "arxiv",
    "version": 1
  }
}