Pith Number

pith:GMMK2OCH

pith:2019:GMMK2OCHCEQIRS7ZNHQ3NSZM6U

not attested not anchored not stored refs pending

Stein's Method for Law of Large Numbers under Sublinear Expectations

Yongsheng Song

arxiv:1904.04674 v1 · 2019-04-09 · 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{GMMK2OCHCEQIRS7ZNHQ3NSZM6U}

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	2026-05-17T23:48:58.454246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3318ad3847112088cbf969e1b6cb2cf50450b5700d83d23b33513f68974afb60

Aliases

arxiv: 1904.04674 · arxiv_version: 1904.04674v1 · doi: 10.48550/arxiv.1904.04674 · pith_short_12: GMMK2OCHCEQI · pith_short_16: GMMK2OCHCEQIRS7Z · pith_short_8: GMMK2OCH

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/GMMK2OCHCEQIRS7ZNHQ3NSZM6U \
  | 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: 3318ad3847112088cbf969e1b6cb2cf50450b5700d83d23b33513f68974afb60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bfbca40347ae53370dae74077ed7ac40ae5a30c0eca7d2650763aec8572701f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-04-09T13:48:10Z",
    "title_canon_sha256": "f25cf451d87148282d6559bf9db0519348831b50e1e1bdc86ba5cb8dc463369d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.04674",
    "kind": "arxiv",
    "version": 1
  }
}