Pith Number

pith:LWZ5FCKW

pith:2011:LWZ5FCKWWMDWQB7JQXDQURNG57

not attested not anchored not stored refs pending

Update of the Borel-Cantelli Lemma

Alexei Stepanov

arxiv:1106.1542 v2 · 2011-06-08 · 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{LWZ5FCKWWMDWQB7JQXDQURNG57}

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	2026-05-18T04:20:15.414410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5db3d28956b3076807e985c70a45a6efe48c724fbbab8a78562f8b3c7f98235c

Aliases

arxiv: 1106.1542 · arxiv_version: 1106.1542v2 · doi: 10.48550/arxiv.1106.1542 · pith_short_12: LWZ5FCKWWMDW · pith_short_16: LWZ5FCKWWMDWQB7J · pith_short_8: LWZ5FCKW

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/LWZ5FCKWWMDWQB7JQXDQURNG57 \
  | 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: 5db3d28956b3076807e985c70a45a6efe48c724fbbab8a78562f8b3c7f98235c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3d6ed06519b438b9bd5965c74ddebde0e17a41eddf4d01f2106f8f89086ee24",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-06-08T11:59:16Z",
    "title_canon_sha256": "6865d6b7821f8d4f4f4f32373df91cf860ea21f661842d1ac8593cea96579c70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.1542",
    "kind": "arxiv",
    "version": 2
  }
}