Pith Number

pith:7G6TGSBF

pith:2012:7G6TGSBFXVLERVI5JVPOPRZDLB

not attested not anchored not stored refs pending

Inequality for Variance of Weighted Sum of Correlated Random Variables and WLLN

Jingwei Liu

arxiv:1209.2275 v8 · 2012-09-11 · math.PR · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7G6TGSBFXVLERVI5JVPOPRZDLB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T02:31:09.162781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9bd334825bd5648d51d4d5ee7c72358740a4228f166ea502793256046ec38f5

Aliases

arxiv: 1209.2275 · arxiv_version: 1209.2275v8 · doi: 10.48550/arxiv.1209.2275 · pith_short_12: 7G6TGSBFXVLE · pith_short_16: 7G6TGSBFXVLERVI5 · pith_short_8: 7G6TGSBF

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/7G6TGSBFXVLERVI5JVPOPRZDLB \
  | 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: f9bd334825bd5648d51d4d5ee7c72358740a4228f166ea502793256046ec38f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "398f82f79439dd39340985a904e703824d52bbf4d01bc39b19bd68b1dbae4fa6",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-09-11T10:04:33Z",
    "title_canon_sha256": "88287da6a4dd71f03051a56771cbc18ad9b619cb23e511228b7e8d76bf9042da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2275",
    "kind": "arxiv",
    "version": 8
  }
}