Pith Number

pith:CI6ODOKV

pith:2010:CI6ODOKVIXGACPNI47GCO7GXMH

not attested not anchored not stored refs pending

Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications

Chenggui Yuan, Feng-Yu Wang

arxiv:1012.5688 v2 · 2010-12-28 · 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{CI6ODOKVIXGACPNI47GCO7GXMH}

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	2026-05-18T04:26:46.692840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

123ce1b95545cc013da8e7cc277cd761cd30be0a7e60536236590835eaef3c17

Aliases

arxiv: 1012.5688 · arxiv_version: 1012.5688v2 · doi: 10.48550/arxiv.1012.5688 · pith_short_12: CI6ODOKVIXGA · pith_short_16: CI6ODOKVIXGACPNI · pith_short_8: CI6ODOKV

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/CI6ODOKVIXGACPNI47GCO7GXMH \
  | 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: 123ce1b95545cc013da8e7cc277cd761cd30be0a7e60536236590835eaef3c17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3db30b1d95fa343cab468f7d75fbd6272d46e9b09e5b145eaaf590887ff06591",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-28T03:14:36Z",
    "title_canon_sha256": "84d67e42c00c36ab94e98158064db353cdd93ed2c3e8a0207d825ea9f48259b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5688",
    "kind": "arxiv",
    "version": 2
  }
}