Pith Number

pith:2Z42RRBQ

pith:2015:2Z42RRBQT7YEEWBH6HQWM3OZID

not attested not anchored not stored refs pending

Two laws of large numbers for sublinear expectations

Chuanfeng Sun, Wenhao Li

arxiv:1511.05631 v2 · 2015-11-18 · 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{2Z42RRBQT7YEEWBH6HQWM3OZID}

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

On nonlinear weak law of large numbers

Receipt and verification

First computed	2026-07-05T07:13:17.622148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d679a8c4309ff0425827f1e1666dd940d6ffd9d2a2949d3805d64c620320423a

Aliases

arxiv: 1511.05631 · arxiv_version: 1511.05631v2 · doi: 10.48550/arxiv.1511.05631 · pith_short_12: 2Z42RRBQT7YE · pith_short_16: 2Z42RRBQT7YEEWBH · pith_short_8: 2Z42RRBQ

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/2Z42RRBQT7YEEWBH6HQWM3OZID \
  | 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: d679a8c4309ff0425827f1e1666dd940d6ffd9d2a2949d3805d64c620320423a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08dfa7737d3be8d378d71010b902204977d895fcc69af5d26ba4f302bb755bd3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-18T00:52:20Z",
    "title_canon_sha256": "729b07b3d559a77f71fb6c902d2c6f2eec58456bfb0491025886a419493a7d08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.05631",
    "kind": "arxiv",
    "version": 2
  }
}