Pith Number

pith:CG7LF3XF

pith:2020:CG7LF3XFW4RYOXIZWLEAPNWZWK

not attested not anchored not stored refs pending

Weak independence of events and the converse of the Borel--Cantelli Lemma

Csaba Bir\'o, Israel R. Curbelo

arxiv:2004.11324 v3 · 2020-04-23 · 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{CG7LF3XFW4RYOXIZWLEAPNWZWK}

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

1 paper in Pith

Efficient Sliced Wasserstein Distance Computation via Adaptive Bayesian Optimization

Receipt and verification

First computed	2026-07-05T03:04:16.071245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11beb2eee5b723875d19b2c807b6d9b28f8032971f48e4ee392a3f5419abd51c

Aliases

arxiv: 2004.11324 · arxiv_version: 2004.11324v3 · doi: 10.48550/arxiv.2004.11324 · pith_short_12: CG7LF3XFW4RY · pith_short_16: CG7LF3XFW4RYOXIZ · pith_short_8: CG7LF3XF

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/CG7LF3XFW4RYOXIZWLEAPNWZWK \
  | 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: 11beb2eee5b723875d19b2c807b6d9b28f8032971f48e4ee392a3f5419abd51c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bded4e86132dfaeef7662c041c42f77828a2463c87fadf5dc2c89fd25a112d2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-04-23T17:18:34Z",
    "title_canon_sha256": "369f2336b7af548a9b55d4d8b42766068cc84eb4b00f6251447f87d85b63d4a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.11324",
    "kind": "arxiv",
    "version": 3
  }
}