Pith Number

pith:YF2A2BJB

pith:2021:YF2A2BJBDCUPIWPKTM4WHVNLDB

not attested not anchored not stored refs pending

Functional relations for higher-order free cumulants

Elba Garcia-Failde, Felix Leid, Ga\"etan Borot, Sergey Shadrin, S\'everin Charbonnier

arxiv:2112.12184 v2 · 2021-12-22 · math.OA · math-ph · math.CO · math.MP · 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{YF2A2BJBDCUPIWPKTM4WHVNLDB}

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	2026-07-05T06:54:35.113052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1740d052118a8f459ea9b3963d5ab184af319be9c7644c16ac698aa037e335b

Aliases

arxiv: 2112.12184 · arxiv_version: 2112.12184v2 · doi: 10.48550/arxiv.2112.12184 · pith_short_12: YF2A2BJBDCUP · pith_short_16: YF2A2BJBDCUPIWPK · pith_short_8: YF2A2BJB

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/YF2A2BJBDCUPIWPKTM4WHVNLDB \
  | 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: c1740d052118a8f459ea9b3963d5ab184af319be9c7644c16ac698aa037e335b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8793d1e535a817c103a3ac242c9ece4da48077f67284c293c81867c84331a5d3",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2021-12-22T19:19:34Z",
    "title_canon_sha256": "d69b237e9989a96ba83d25da3e55864ff1de5dba3c8c973785a86304a8703560"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.12184",
    "kind": "arxiv",
    "version": 2
  }
}