Pith Number

pith:RINT7UOX

pith:2016:RINT7UOX2K445F5SELDDBIWU3J

not attested not anchored not stored refs pending

Free cumulants, Schr\"oder trees, and operads

Fr\'ed\'eric Menous, Jean-Christophe Novelli, Jean-Yves Thibon, Matthieu Josuat-Verg\`es

arxiv:1604.04759 v2 · 2016-04-16 · 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{RINT7UOX2K445F5SELDDBIWU3J}

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	2026-05-18T00:44:01.220597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a1b3fd1d7d2b9ce97b222c630a2d4da57d61fbd5f952ea945db05bf8b966814

Aliases

arxiv: 1604.04759 · arxiv_version: 1604.04759v2 · doi: 10.48550/arxiv.1604.04759 · pith_short_12: RINT7UOX2K44 · pith_short_16: RINT7UOX2K445F5S · pith_short_8: RINT7UOX

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/RINT7UOX2K445F5SELDDBIWU3J \
  | 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: 8a1b3fd1d7d2b9ce97b222c630a2d4da57d61fbd5f952ea945db05bf8b966814

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54b108626f9387eacbf81e96d54df5eb98636500be6da60e89f2b4ba9b4e325c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-04-16T14:32:13Z",
    "title_canon_sha256": "d5d22553d7260c2f6fcbfb7d34a7dac673abe4ed66b03fc6877e7fbd711223c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.04759",
    "kind": "arxiv",
    "version": 2
  }
}