Pith Number

pith:27TEUR6S

pith:2012:27TEUR6SKMYKE2CJIZH4XDW2F2

not attested not anchored not stored refs pending

Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations

Ling Zhou, Ze-Chun Hu

arxiv:1211.1090 v2 · 2012-11-06 · 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{27TEUR6SKMYKE2CJIZH4XDW2F2}

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	2026-05-18T03:20:35.419640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7e64a47d25330a26849464fcb8eda2e9bd13083afcdb44534caa2be5cbc75e2

Aliases

arxiv: 1211.1090 · arxiv_version: 1211.1090v2 · doi: 10.48550/arxiv.1211.1090 · pith_short_12: 27TEUR6SKMYK · pith_short_16: 27TEUR6SKMYKE2CJ · pith_short_8: 27TEUR6S

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/27TEUR6SKMYKE2CJIZH4XDW2F2 \
  | 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: d7e64a47d25330a26849464fcb8eda2e9bd13083afcdb44534caa2be5cbc75e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "962ddb10b17fe39c078b8ee4a62575f14db21fd87f0a3bb2593a70f84c199144",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-06T02:33:17Z",
    "title_canon_sha256": "bf354f1599550027afedfcba0f2700f16661409f3df5b4d1ebfdd4d4e224a42e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1090",
    "kind": "arxiv",
    "version": 2
  }
}