Pith Number

pith:4GSCEAS4

pith:2009:4GSCEAS4GFEIC2QC5HJBYOV3BG

not attested not anchored not stored refs pending

New estimates of the convergence rate in the Lyapunov theorem

Ilya Tyurin

arxiv:0912.0726 v1 · 2009-12-03 · 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{4GSCEAS4GFEIC2QC5HJBYOV3BG}

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

2 papers in Pith

Bracketing Relationships of Weighted Average Treatment Effects

Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Proven

Receipt and verification

First computed	2026-07-04T17:17:03.490139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1a422025c3148816a02e9d21c3abb09a9fb8febbef133da0346c184b9779ebb

Aliases

arxiv: 0912.0726 · arxiv_version: 0912.0726v1 · doi: 10.48550/arxiv.0912.0726 · pith_short_12: 4GSCEAS4GFEI · pith_short_16: 4GSCEAS4GFEIC2QC · pith_short_8: 4GSCEAS4

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/4GSCEAS4GFEIC2QC5HJBYOV3BG \
  | 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: e1a422025c3148816a02e9d21c3abb09a9fb8febbef133da0346c184b9779ebb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a592905ab7d866e2ef1acedeb5e8b239323900dd384297545905bd3ee9f5f793",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-12-03T20:25:50Z",
    "title_canon_sha256": "11de408cf541798d27933d64984ee540263af838a694810b0152b0cdbba139db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0726",
    "kind": "arxiv",
    "version": 1
  }
}