Pith Number

pith:AJ57J3B2

pith:2012:AJ57J3B2VROFBDK2KJ4XLDPRIJ

not attested not anchored not stored refs pending

Some inequalities and limit theorems under sublinear expectations

Yan-Zhi Yang, Ze-Chun Hu

arxiv:1207.0489 v4 · 2012-07-02 · 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{AJ57J3B2VROFBDK2KJ4XLDPRIJ}

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	2026-05-18T01:44:20.880534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

027bf4ec3aac5c508d5a5279758df1427a0418615334a21dd4bfa56f8ca86bc4

Aliases

arxiv: 1207.0489 · arxiv_version: 1207.0489v4 · doi: 10.48550/arxiv.1207.0489 · pith_short_12: AJ57J3B2VROF · pith_short_16: AJ57J3B2VROFBDK2 · pith_short_8: AJ57J3B2

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/AJ57J3B2VROFBDK2KJ4XLDPRIJ \
  | 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: 027bf4ec3aac5c508d5a5279758df1427a0418615334a21dd4bfa56f8ca86bc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44bd579ed68d706c5ae8d90f4fd5f1f982eafdef5c706bccf4b4986fca6dbb08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-07-02T04:00:12Z",
    "title_canon_sha256": "45fe6dfb219d92496bf4b1b7606bf8c6a337f58c6ab57472b07b5d55f5f46162"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0489",
    "kind": "arxiv",
    "version": 4
  }
}