Pith Number

pith:XUTYY24I

pith:2016:XUTYY24IDAI6D3T57DAF6GKO22

not attested not anchored not stored refs pending

Governing equations for Probability densities of stochastic differential equations with discrete time delays

Xu Sun, Yayun Zheng

arxiv:1609.03186 v1 · 2016-09-11 · math.DS · 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{XUTYY24IDAI6D3T57DAF6GKO22}

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	2026-05-18T01:04:47.576208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd278c6b881811e1ee7df8c05f194ed6aafd3fe23ae0c2efeda9ebe463c4ca51

Aliases

arxiv: 1609.03186 · arxiv_version: 1609.03186v1 · doi: 10.48550/arxiv.1609.03186 · pith_short_12: XUTYY24IDAI6 · pith_short_16: XUTYY24IDAI6D3T5 · pith_short_8: XUTYY24I

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/XUTYY24IDAI6D3T57DAF6GKO22 \
  | 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: bd278c6b881811e1ee7df8c05f194ed6aafd3fe23ae0c2efeda9ebe463c4ca51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4ff7e1385f6a5d3477f54443f240435e0d2df7f56ff9a5c1b36d5a49bd54b9e",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-09-11T17:29:43Z",
    "title_canon_sha256": "8923ecdd5640540da3d65f0c2c4ccf09aae7d40b40ddcaddca227de09a19b14a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03186",
    "kind": "arxiv",
    "version": 1
  }
}