Pith Number

pith:4Q47APYP

pith:2010:4Q47APYP24WKSQPLC3AMCI4ACQ

not attested not anchored not stored refs pending

The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation

Emanuele Dolera, Eugenio Regazzini

arxiv:1009.3406 v1 · 2010-09-17 · 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{4Q47APYP24WKSQPLC3AMCI4ACQ}

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	2026-05-18T01:04:58.377651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e439f03f0fd72ca941eb16c0c12380142a907148b3031e38915c3f4df91f861d

Aliases

arxiv: 1009.3406 · arxiv_version: 1009.3406v1 · doi: 10.48550/arxiv.1009.3406 · pith_short_12: 4Q47APYP24WK · pith_short_16: 4Q47APYP24WKSQPL · pith_short_8: 4Q47APYP

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/4Q47APYP24WKSQPLC3AMCI4ACQ \
  | 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: e439f03f0fd72ca941eb16c0c12380142a907148b3031e38915c3f4df91f861d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e02982a79ebd6c1af26d197b13072b2a34a1f89891cd137c6794b65d384c504",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-09-17T12:09:09Z",
    "title_canon_sha256": "2fe45df910031979d99534f8dcfd9e464a82ecbb7f667b0b8dd50845e3a276ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3406",
    "kind": "arxiv",
    "version": 1
  }
}