Pith Number

pith:YVPPR3NG

pith:2011:YVPPR3NGCTBNWIWBNNG6GBKXH3

not attested not anchored not stored refs pending

New limit theorems related to free multiplicative convolution

Hiroaki Yoshida, Noriyoshi Sakuma

arxiv:1103.6156 v2 · 2011-03-31 · 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{YVPPR3NGCTBNWIWBNNG6GBKXH3}

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	2026-05-18T03:30:15.106350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c55ef8eda614c2db22c16b4de305573eef6bbccf40e7674fef22bcff359054a3

Aliases

arxiv: 1103.6156 · arxiv_version: 1103.6156v2 · doi: 10.48550/arxiv.1103.6156 · pith_short_12: YVPPR3NGCTBN · pith_short_16: YVPPR3NGCTBNWIWB · pith_short_8: YVPPR3NG

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/YVPPR3NGCTBNWIWBNNG6GBKXH3 \
  | 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: c55ef8eda614c2db22c16b4de305573eef6bbccf40e7674fef22bcff359054a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b43412defc2e78b9ea993a2f93f9ae43ce89535c1e5ba254bccb302efb847aa6",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-31T12:19:50Z",
    "title_canon_sha256": "d87c8f42cb1246cc1bc98cf2df2d17e145a7b0d00fa191d28539f39a4f9e5205"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.6156",
    "kind": "arxiv",
    "version": 2
  }
}