Pith Number

pith:LBUHMIXX

pith:2008:LBUHMIXXA6C26Z6K7LTZJLWQBD

not attested not anchored not stored refs pending

Limits Laws for Geometric Means of Free Random Variables

Gabriel H. Tucci

arxiv:0802.4226 v2 · 2008-02-28 · 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{LBUHMIXXA6C26Z6K7LTZJLWQBD}

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	2026-05-18T04:39:59.805725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58687622f70785af67cafae794aed008c428cc2baa1ce1fc968eb4a00e87cfb8

Aliases

arxiv: 0802.4226 · arxiv_version: 0802.4226v2 · doi: 10.48550/arxiv.0802.4226 · pith_short_12: LBUHMIXXA6C2 · pith_short_16: LBUHMIXXA6C26Z6K · pith_short_8: LBUHMIXX

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/LBUHMIXXA6C26Z6K7LTZJLWQBD \
  | 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: 58687622f70785af67cafae794aed008c428cc2baa1ce1fc968eb4a00e87cfb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "116591c3394b77591f0e514974caaaab12e59f03b5aeb1cbccc9aeacb48378ca",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2008-02-28T16:25:42Z",
    "title_canon_sha256": "cece0d10028af6f995653f41fca0603950b90755d9fa2f932abc8f90eb0cd832"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.4226",
    "kind": "arxiv",
    "version": 2
  }
}