Pith Number

pith:WOGGBQRQ

pith:2009:WOGGBQRQLYHSHTKE3O326BSJ5H

not attested not anchored not stored refs pending

Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds

Feng-Yu Wang

arxiv:0911.1644 v4 · 2009-11-09 · math.PR · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WOGGBQRQLYHSHTKE3O326BSJ5H}

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	2026-05-18T03:40:37.011260Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b38c60c2305e0f23cd44dbb7af0649e9d39521936cd874742426b3fe553b1996

Aliases

arxiv: 0911.1644 · arxiv_version: 0911.1644v4 · doi: 10.48550/arxiv.0911.1644 · pith_short_12: WOGGBQRQLYHS · pith_short_16: WOGGBQRQLYHSHTKE · pith_short_8: WOGGBQRQ

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/WOGGBQRQLYHSHTKE3O326BSJ5H \
  | 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: b38c60c2305e0f23cd44dbb7af0649e9d39521936cd874742426b3fe553b1996

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e351e98267aa47a7579e41dedf22a1e3967dc38129776ddd5200b8b0bed031ff",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-11-09T11:41:38Z",
    "title_canon_sha256": "668b77c6194005e084bd7ceddfc57b2bddb53b72da42ff7a342589cf1482530a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.1644",
    "kind": "arxiv",
    "version": 4
  }
}