Pith Number

pith:2DIV5OMC

pith:2007:2DIV5OMCDRKARND6S7FCQUG6F5

not attested not anchored not stored refs pending

On the rate of convergence and Berry-Esseen type theorems for a multivariate free central limit theorem

Roland Speicher

arxiv:0712.2974 v1 · 2007-12-18 · math.OA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2DIV5OMCDRKARND6S7FCQUG6F5}

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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.

Cited by

1 paper in Pith

Rates of convergence in the Free Multiplicative Central Limit Theorem

Receipt and verification

First computed	2026-07-04T15:06:21.581199Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0d15eb9821c5408b47e97ca2850de2f6c9dcd988f30957d1700d95e2048d86c

Aliases

arxiv: 0712.2974 · arxiv_version: 0712.2974v1 · doi: 10.48550/arxiv.0712.2974 · pith_short_12: 2DIV5OMCDRKA · pith_short_16: 2DIV5OMCDRKARND6 · pith_short_8: 2DIV5OMC

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/2DIV5OMCDRKARND6S7FCQUG6F5 \
  | 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: d0d15eb9821c5408b47e97ca2850de2f6c9dcd988f30957d1700d95e2048d86c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e6ff6cd5c472dafc95f65e8a99f6f8b15c786968c769353e6329ede57e28593",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2007-12-18T14:36:41Z",
    "title_canon_sha256": "d1d8288cfa85d1148cc3a265208964d3377cb713d436d5532102c270f5fc04d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.2974",
    "kind": "arxiv",
    "version": 1
  }
}