Pith Number

pith:HYHWBWLH

pith:2011:HYHWBWLHKJSXM2K7FIZJT7F7DU

not attested not anchored not stored refs pending

Convergence of random series and the rate of convergence of the strong law of large numbers in game-theoretic probability

Akimichi Takemura, Kenshi Miyabe

arxiv:1103.1426 v4 · 2011-03-08 · 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{HYHWBWLHKJSXM2K7FIZJT7F7DU}

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	2026-05-18T04:07:54.135002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e0f60d967526576695f2a3299fcbf1d37a590effbd5ae8a362a530aacb69eb4

Aliases

arxiv: 1103.1426 · arxiv_version: 1103.1426v4 · doi: 10.48550/arxiv.1103.1426 · pith_short_12: HYHWBWLHKJSX · pith_short_16: HYHWBWLHKJSXM2K7 · pith_short_8: HYHWBWLH

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/HYHWBWLHKJSXM2K7FIZJT7F7DU \
  | 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: 3e0f60d967526576695f2a3299fcbf1d37a590effbd5ae8a362a530aacb69eb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea02253bf1e57826cf468aa4198dd5eb2588ae90d7b92c44068ac7c81dde9880",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-08T03:39:43Z",
    "title_canon_sha256": "f72cfdc00568613b5cd729bd804d60cc463bd9382e0eebce3bf62591346693a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1426",
    "kind": "arxiv",
    "version": 4
  }
}