Pith Number

pith:B3WRMLVN

pith:2014:B3WRMLVNC6WF7HFE75472OUAEX

not attested not anchored not stored refs pending

Cumulants, free cumulants and half-shuffles

Frederic Patras, Kurusch Ebrahimi-Fard

arxiv:1409.5664 v2 · 2014-09-19 · 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{B3WRMLVNC6WF7HFE75472OUAEX}

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	2026-05-18T02:23:26.710220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0eed162ead17ac5f9ca4ff79fd3a8025fc84b76eba02d834c74e04947034bfd4

Aliases

arxiv: 1409.5664 · arxiv_version: 1409.5664v2 · doi: 10.48550/arxiv.1409.5664 · pith_short_12: B3WRMLVNC6WF · pith_short_16: B3WRMLVNC6WF7HFE · pith_short_8: B3WRMLVN

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/B3WRMLVNC6WF7HFE75472OUAEX \
  | 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: 0eed162ead17ac5f9ca4ff79fd3a8025fc84b76eba02d834c74e04947034bfd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e26b69010ee6476a3e27ef7a64abf37a7d10e42cf09e6eeb6ee2425a26aac399",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-19T14:17:23Z",
    "title_canon_sha256": "7e5eca601dda3d0f910decdad3892889b896e0e3f9da871c4578565e98ea4c12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.5664",
    "kind": "arxiv",
    "version": 2
  }
}