Pith Number

pith:ZUBR6A3Q

pith:2018:ZUBR6A3QLQPHO4KI2U76OTEOWC

not attested not anchored not stored refs pending

Convergence rates in the law of large numbers and new kinds of convergence of random variables

Wei Sun, Ze-Chun Hu

arxiv:1805.02803 v2 · 2018-05-08 · 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{ZUBR6A3QLQPHO4KI2U76OTEOWC}

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	2026-05-18T00:13:10.091608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd031f03705c1e777148d53fe74c8eb0a3dff72887da622f1fd53894359af535

Aliases

arxiv: 1805.02803 · arxiv_version: 1805.02803v2 · doi: 10.48550/arxiv.1805.02803 · pith_short_12: ZUBR6A3QLQPH · pith_short_16: ZUBR6A3QLQPHO4KI · pith_short_8: ZUBR6A3Q

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/ZUBR6A3QLQPHO4KI2U76OTEOWC \
  | 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: cd031f03705c1e777148d53fe74c8eb0a3dff72887da622f1fd53894359af535

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4641215611d26e99c9b4af271e34d0ecc0f21489b88af36ca997f92383deeb14",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-05-08T01:58:50Z",
    "title_canon_sha256": "c6579e8d5dc2bb58129fd2d0bde5d18ef471a15ca09f931b20a34574da7bfc5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.02803",
    "kind": "arxiv",
    "version": 2
  }
}