Pith Number

pith:KLM7OYWH

pith:2016:KLM7OYWHM4FI7DCCHHGKZ3ASBE

not attested not anchored not stored refs pending

On Complete Convergence in Mean for Double Sums of Independent Random Elements in Banach Spaces

Le Van Thanh, Nguyen Thi Thuy

arxiv:1606.01725 v1 · 2016-06-06 · 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{KLM7OYWHM4FI7DCCHHGKZ3ASBE}

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	2026-05-18T01:12:53.728630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52d9f762c7670a8f8c4239ccacec12093f3e5aa326a64bda595259afbba45f21

Aliases

arxiv: 1606.01725 · arxiv_version: 1606.01725v1 · doi: 10.48550/arxiv.1606.01725 · pith_short_12: KLM7OYWHM4FI · pith_short_16: KLM7OYWHM4FI7DCC · pith_short_8: KLM7OYWH

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/KLM7OYWHM4FI7DCCHHGKZ3ASBE \
  | 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: 52d9f762c7670a8f8c4239ccacec12093f3e5aa326a64bda595259afbba45f21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b37cc97f47437e63ab8a8e0d38cb8bcef555a462829ae4219c81488d85578b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-06-06T13:07:55Z",
    "title_canon_sha256": "06d9682e7f65ba992931659f19c9bb7f34b06c0c3cc5775006c09abfcab110cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.01725",
    "kind": "arxiv",
    "version": 1
  }
}