Pith Number

pith:ZF5GYS3D

pith:2019:ZF5GYS3DVT7LJLXOTXGZ5R6U6V

not attested not anchored not stored refs pending

Products of Conditional Expectation Operators: Convergence and Divergence

Guolie Lan, Wei Sun, Ze-Chun Hu

arxiv:1903.03917 v3 · 2019-03-10 · 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{ZF5GYS3DVT7LJLXOTXGZ5R6U6V}

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	2026-05-17T23:41:24.550086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c97a6c4b63acfeb4aeee9dcd9ec7d4f5517bba63bc330063abb25a978f53c834

Aliases

arxiv: 1903.03917 · arxiv_version: 1903.03917v3 · doi: 10.48550/arxiv.1903.03917 · pith_short_12: ZF5GYS3DVT7L · pith_short_16: ZF5GYS3DVT7LJLXO · pith_short_8: ZF5GYS3D

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/ZF5GYS3DVT7LJLXOTXGZ5R6U6V \
  | 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: c97a6c4b63acfeb4aeee9dcd9ec7d4f5517bba63bc330063abb25a978f53c834

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "773778f40b200fbca2c505e8c0b18de22fa16cdaad59735bc7ad97a95328ee54",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-03-10T03:59:44Z",
    "title_canon_sha256": "4a2968fda96199c1be88f075b2b1f0f5fc7d439a0d7636ce8d2301eed8beb6da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.03917",
    "kind": "arxiv",
    "version": 3
  }
}