Pith Number

pith:Q3FFGPFK

pith:2011:Q3FFGPFKIWSFVCL5IEJHD5LI2S

not attested not anchored not stored refs pending

Central Limit for the Product of Free Random Variables

Keang-Po Ho

arxiv:1101.5220 v3 · 2011-01-27 · math.OA · 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{Q3FFGPFKIWSFVCL5IEJHD5LI2S}

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	2026-05-18T02:40:46.012130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86ca533caa45a45a897d411271f568d4ba59ea246089678e2cc6879092ba9e02

Aliases

arxiv: 1101.5220 · arxiv_version: 1101.5220v3 · doi: 10.48550/arxiv.1101.5220 · pith_short_12: Q3FFGPFKIWSF · pith_short_16: Q3FFGPFKIWSFVCL5 · pith_short_8: Q3FFGPFK

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/Q3FFGPFKIWSFVCL5IEJHD5LI2S \
  | 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: 86ca533caa45a45a897d411271f568d4ba59ea246089678e2cc6879092ba9e02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f075ed530b00e29d16f9ebc47626038b0f7cf5ca9e099a3c611c6dc353bba46f",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-01-27T08:10:32Z",
    "title_canon_sha256": "e4ea84279b8bb6ac461fd5a2b73b5e33bee4b0efe2a09f0d293fa0cd1b945327"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5220",
    "kind": "arxiv",
    "version": 3
  }
}