Pith Number

pith:M2STEMBE

pith:2025:M2STEMBEGTQ6LM3OW4BQHFQIPH

not attested not anchored not stored refs pending

Tree-indexed sums of Catalan numbers

Alin Bostan, Paul Th\'evenin, Valentin F\'eray

arxiv:2507.23557 v1 · 2025-07-31 · math.CO · cs.SC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M2STEMBEGTQ6LM3OW4BQHFQIPH}

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	2026-07-05T11:46:26.820925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66a532302434e1e5b36eb70303960879db13dab6d13563bbda01fae384fd4377

Aliases

arxiv: 2507.23557 · arxiv_version: 2507.23557v1 · doi: 10.48550/arxiv.2507.23557 · pith_short_12: M2STEMBEGTQ6 · pith_short_16: M2STEMBEGTQ6LM3O · pith_short_8: M2STEMBE

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/M2STEMBEGTQ6LM3OW4BQHFQIPH \
  | 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: 66a532302434e1e5b36eb70303960879db13dab6d13563bbda01fae384fd4377

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d7349b3c0137751463dabb0d21cb0672e792066c09946a41935357da6c413b9",
    "cross_cats_sorted": [
      "cs.SC",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-31T13:46:17Z",
    "title_canon_sha256": "5ac960be9b7cbb2d963dca4621c8abffe01579ec0b6d74a4df2b6049cc718994"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.23557",
    "kind": "arxiv",
    "version": 1
  }
}