Pith Number

pith:OSR2LHCM

pith:2012:OSR2LHCM3XCWKLDPHBRNYLTGNN

not attested not anchored not stored refs pending

Integration by Parts Formula and Shift Harnack Inequality for Stochastic Equations

Feng-Yu Wang

arxiv:1203.4023 v4 · 2012-03-19 · 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{OSR2LHCM3XCWKLDPHBRNYLTGNN}

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	2026-05-18T02:55:18.754604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74a3a59c4cddc5652c6f3862dc2e666b7233f565b872aea4eefbdc400a6e4b76

Aliases

arxiv: 1203.4023 · arxiv_version: 1203.4023v4 · doi: 10.48550/arxiv.1203.4023 · pith_short_12: OSR2LHCM3XCW · pith_short_16: OSR2LHCM3XCWKLDP · pith_short_8: OSR2LHCM

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/OSR2LHCM3XCWKLDPHBRNYLTGNN \
  | 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: 74a3a59c4cddc5652c6f3862dc2e666b7233f565b872aea4eefbdc400a6e4b76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2dc10ffb3b00af1b35eaa712bad42d3eae3988e30377b7ec3a0b4febf7a9483",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-19T02:51:51Z",
    "title_canon_sha256": "86fd5b536b8fd92a346959f44e4bbc2ac4a77aa26345f8e344b61be0513d0a49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4023",
    "kind": "arxiv",
    "version": 4
  }
}