Pith Number

pith:XRV4Z2XD

pith:2011:XRV4Z2XDZLLYAZKK25BCUXXVLJ

not attested not anchored not stored refs pending

On the Coupling Property and the Liouville Theorem for Ornstein-Uhlenbeck Processes

Jian Wang, Ren\'e L. Schilling

arxiv:1104.2166 v2 · 2011-04-12 · math.PR · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XRV4Z2XDZLLYAZKK25BCUXXVLJ}

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	2026-05-18T04:22:00.495135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc6bcceae3cad780654ad7422a5ef55a47d5a9d8abc180578adec7f888bfd30b

Aliases

arxiv: 1104.2166 · arxiv_version: 1104.2166v2 · doi: 10.48550/arxiv.1104.2166 · pith_short_12: XRV4Z2XDZLLY · pith_short_16: XRV4Z2XDZLLYAZKK · pith_short_8: XRV4Z2XD

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/XRV4Z2XDZLLYAZKK25BCUXXVLJ \
  | 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: bc6bcceae3cad780654ad7422a5ef55a47d5a9d8abc180578adec7f888bfd30b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00bec3bf866241315732711f0508004eac2db5d6eab49d468c855f9c3a7512d2",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-04-12T11:01:58Z",
    "title_canon_sha256": "4a76b423760cf9e63e13af3a0ed38cc35330613d01c5bca1802e530e61ed8813"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2166",
    "kind": "arxiv",
    "version": 2
  }
}