Pith Number

pith:K7MGFRKH

pith:2011:K7MGFRKHGDC7YRLIPWRY47LEB6

not attested not anchored not stored refs pending

Weak Limit of the Geometric Sum of Independent But Not Identically Distributed Random Variables

Alexis Akira Toda

arxiv:1111.1786 v2 · 2011-11-08 · math.PR · stat.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K7MGFRKHGDC7YRLIPWRY47LEB6}

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

Stein's method for asymmetric Laplace approximation

Receipt and verification

First computed	2026-05-18T04:04:07.799511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57d862c54730c5fc45687da38e7d640f9dee5e713abd3ab075eec27edf5a76ae

Aliases

arxiv: 1111.1786 · arxiv_version: 1111.1786v2 · doi: 10.48550/arxiv.1111.1786 · pith_short_12: K7MGFRKHGDC7 · pith_short_16: K7MGFRKHGDC7YRLI · pith_short_8: K7MGFRKH

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/K7MGFRKHGDC7YRLIPWRY47LEB6 \
  | 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: 57d862c54730c5fc45687da38e7d640f9dee5e713abd3ab075eec27edf5a76ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1a0a65935096b31c9d94393bb1b5059352ae4a18a668b2680389e406ce9d756",
    "cross_cats_sorted": [
      "stat.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-08T03:11:49Z",
    "title_canon_sha256": "88d3aad51e6975023d8064d4df804837737b702fb15fd797716a4defc4440ef9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1786",
    "kind": "arxiv",
    "version": 2
  }
}