Pith Number

pith:FWE4P75S

pith:2012:FWE4P75S7WOSWU2SW4YCLL3STZ

not attested not anchored not stored refs pending

The law of large numbers for the free multiplicative convolution

S\"oren M\"oller, Uffe Haagerup

arxiv:1211.4457 v2 · 2012-11-19 · 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{FWE4P75S7WOSWU2SW4YCLL3STZ}

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.

Cited by

1 paper in Pith

Free compressions of R-diagonal random variables and the semigroup of Brown measures

Receipt and verification

First computed	2026-05-18T03:04:22.621805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d89c7ffb2fd9d2b5352b73025af729e534f2e0284ae10005e57814c91ec0a48

Aliases

arxiv: 1211.4457 · arxiv_version: 1211.4457v2 · doi: 10.48550/arxiv.1211.4457 · pith_short_12: FWE4P75S7WOS · pith_short_16: FWE4P75S7WOSWU2S · pith_short_8: FWE4P75S

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/FWE4P75S7WOSWU2SW4YCLL3STZ \
  | 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: 2d89c7ffb2fd9d2b5352b73025af729e534f2e0284ae10005e57814c91ec0a48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7a9b0048e9e0f94fbae2945e9d378df80637656a586af276e166814e8952989",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-11-19T15:16:59Z",
    "title_canon_sha256": "e281359485971709bb9a396ac0021fcd4298a88d9124507bfd1ac1b20b751142"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4457",
    "kind": "arxiv",
    "version": 2
  }
}