Pith Number

pith:WCJV2HWE

pith:2016:WCJV2HWECNJMBQKQRXSQWK5M5S

not attested not anchored not stored refs pending

Integration by Parts formula for SPDEs with Multiplicative Noise and its Applications

Li-Xia Liu, Shao-Qin Zhang, Xing Huang

arxiv:1610.02778 v1 · 2016-10-10 · 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{WCJV2HWECNJMBQKQRXSQWK5M5S}

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	2026-05-18T01:02:50.746156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0935d1ec41352c0c1508de50b2bacecb72e2d69ea4f61770080238c0b64df50

Aliases

arxiv: 1610.02778 · arxiv_version: 1610.02778v1 · doi: 10.48550/arxiv.1610.02778 · pith_short_12: WCJV2HWECNJM · pith_short_16: WCJV2HWECNJMBQKQ · pith_short_8: WCJV2HWE

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/WCJV2HWECNJMBQKQRXSQWK5M5S \
  | 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: b0935d1ec41352c0c1508de50b2bacecb72e2d69ea4f61770080238c0b64df50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "558a7b0b79f7df17d8557e7aafb030d39732396073ae0c4a21cf5ebc7dffbe02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-10T06:05:59Z",
    "title_canon_sha256": "ea9f56c4a95c30bf39cb613a6d1104bbee4c429120320d5f4d818e091db7e8ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.02778",
    "kind": "arxiv",
    "version": 1
  }
}