Pith Number

pith:O6UGOZQC

pith:2013:O6UGOZQCT75TVBMP2GJ5A5TQAV

not attested not anchored not stored refs pending

The Borel-Cantelli Lemma for Markov Sequences of Events

Alexei Stepanov

arxiv:1306.3750 v2 · 2013-06-17 · stat.ME · 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{O6UGOZQCT75TVBMP2GJ5A5TQAV}

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	2026-05-18T03:00:39.413867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77a86766029ffb3a858fd193d07670054b229d5a80a8d0d32391401cbfb033ee

Aliases

arxiv: 1306.3750 · arxiv_version: 1306.3750v2 · doi: 10.48550/arxiv.1306.3750 · pith_short_12: O6UGOZQCT75T · pith_short_16: O6UGOZQCT75TVBMP · pith_short_8: O6UGOZQC

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/O6UGOZQCT75TVBMP2GJ5A5TQAV \
  | 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: 77a86766029ffb3a858fd193d07670054b229d5a80a8d0d32391401cbfb033ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbacb885a041f31e1c22c0f0a0f4a3773b26dc9b7ce9561a790af8ed8bd63570",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2013-06-17T06:48:36Z",
    "title_canon_sha256": "2fe1755893b9134de0ec58cd19fc582afc11bf0b747edf16f317767b03c36b62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3750",
    "kind": "arxiv",
    "version": 2
  }
}