Pith Number

pith:SDD5R7NH

pith:2011:SDD5R7NHVUG7SQ3OZ45VORIUPN

not attested not anchored not stored refs pending

The Independence under Sublinear Expectations

Mingshang Hu

arxiv:1107.0361 v1 · 2011-07-02 · 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{SDD5R7NHVUG7SQ3OZ45VORIUPN}

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	2026-05-18T04:18:54.109457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90c7d8fda7ad0df9436ecf3b5745147b4cecedf23da2379bbfbb6505c3653310

Aliases

arxiv: 1107.0361 · arxiv_version: 1107.0361v1 · doi: 10.48550/arxiv.1107.0361 · pith_short_12: SDD5R7NHVUG7 · pith_short_16: SDD5R7NHVUG7SQ3O · pith_short_8: SDD5R7NH

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/SDD5R7NHVUG7SQ3OZ45VORIUPN \
  | 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: 90c7d8fda7ad0df9436ecf3b5745147b4cecedf23da2379bbfbb6505c3653310

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59258b376df94e10dfdaaadb8ced3c8f21c39c3e936137c3f8d59cb8521382d5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-02T05:20:00Z",
    "title_canon_sha256": "cf45b20cbf8f233a9b960b6a189d76a03b1aabb031a60920dc0551045d6dfcd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0361",
    "kind": "arxiv",
    "version": 1
  }
}