Pith Number

pith:VVLDQF2A

pith:2025:VVLDQF2ADNCDHSTKS3DYPK3BZI

not attested not anchored not stored refs pending

Rates of convergence in the Free Multiplicative Central Limit Theorem

Marwa Banna, Nicolas Gilliers, Pei-Lun Tseng

arxiv:2505.18348 v2 · 2025-05-23 · 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{VVLDQF2ADNCDHSTKS3DYPK3BZI}

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	2026-07-05T11:30:44.102932Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad563817401b4433ca6a96c787ab61ca28925c7c728ba7072e99b02f66265be6

Aliases

arxiv: 2505.18348 · arxiv_version: 2505.18348v2 · doi: 10.48550/arxiv.2505.18348 · pith_short_12: VVLDQF2ADNCD · pith_short_16: VVLDQF2ADNCDHSTK · pith_short_8: VVLDQF2A

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/VVLDQF2ADNCDHSTKS3DYPK3BZI \
  | 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: ad563817401b4433ca6a96c787ab61ca28925c7c728ba7072e99b02f66265be6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3724f309e544f5f90c83ef499136476ee500f2b81a329e7c475bd83f8c0592a",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2025-05-23T20:09:51Z",
    "title_canon_sha256": "a0673f56d527b54adc585dc067adea7f2daa9bdb183402a0cab7c702039d21c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.18348",
    "kind": "arxiv",
    "version": 2
  }
}