Pith Number

pith:7E75XGJH

pith:2011:7E75XGJHG7DFNAGPOXZTEK6KES

not attested not anchored not stored refs pending

Central and non-central limit theorems in a free probability setting

Ivan Nourdin (IECN), Murad Taqqu

arxiv:1110.2703 v4 · 2011-10-12 · math.PR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7E75XGJHG7DFNAGPOXZTEK6KES}

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	2026-05-18T03:54:39.288996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f93fdb992737c65680cf75f3322bca24b84e0183f664ca94ca4bad7b71b950ea

Aliases

arxiv: 1110.2703 · arxiv_version: 1110.2703v4 · doi: 10.48550/arxiv.1110.2703 · pith_short_12: 7E75XGJHG7DF · pith_short_16: 7E75XGJHG7DFNAGP · pith_short_8: 7E75XGJH

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/7E75XGJHG7DFNAGPOXZTEK6KES \
  | 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: f93fdb992737c65680cf75f3322bca24b84e0183f664ca94ca4bad7b71b950ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb590ab4ee9af9295c71cd737bca365f7c6846b9def3eb6bf2f4798c36e90306",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-10-12T17:05:21Z",
    "title_canon_sha256": "8c1048651bb987bdfcf84c2b6528931dd113f23d29b452fdf2b172871b7f4ece"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2703",
    "kind": "arxiv",
    "version": 4
  }
}