Pith Number

pith:PJU2KJEI

pith:2014:PJU2KJEILZIN2B2Y3J7MHG7Q2R

not attested not anchored not stored refs pending

Smoothness of density for stochastic differential equations with Markovian switching

David Nualart, Xiaobin Sun, Yaozhong Hu, Yingchao Xie

arxiv:1409.3927 v2 · 2014-09-13 · 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{PJU2KJEILZIN2B2Y3J7MHG7Q2R}

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	2026-05-18T00:32:31.673885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a69a524885e50dd0758da7ec39bf0d4639b89a15bb38395fff7a0524595d9ef

Aliases

arxiv: 1409.3927 · arxiv_version: 1409.3927v2 · doi: 10.48550/arxiv.1409.3927 · pith_short_12: PJU2KJEILZIN · pith_short_16: PJU2KJEILZIN2B2Y · pith_short_8: PJU2KJEI

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/PJU2KJEILZIN2B2Y3J7MHG7Q2R \
  | 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: 7a69a524885e50dd0758da7ec39bf0d4639b89a15bb38395fff7a0524595d9ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e46c71f1035ee552a57a09f7f9ba7c7d87133f4723619fc9c06706b7eb7a8375",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-09-13T09:25:14Z",
    "title_canon_sha256": "f514d10cb4da0e380f883462b7a57545d2295a2b11fd672da94886304f62b5a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.3927",
    "kind": "arxiv",
    "version": 2
  }
}