Pith Number

pith:3B4X37YI

pith:2016:3B4X37YI2ABRP5W4PCRG5ZB6MZ

not attested not anchored not stored refs pending

Strong convergence rate in averaging principle for stochastic hyperbolic-parabolic equations with two time-scales

Hongbo Fu, Jicheng Liu, Li Wan, Xianming Liu

arxiv:1611.09080 v2 · 2016-11-28 · 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{3B4X37YI2ABRP5W4PCRG5ZB6MZ}

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	2026-05-18T00:27:30.603944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8797dff08d00317f6dc78a26ee43e6677d7cea230a429ee79048f18bb85b8e6

Aliases

arxiv: 1611.09080 · arxiv_version: 1611.09080v2 · doi: 10.48550/arxiv.1611.09080 · pith_short_12: 3B4X37YI2ABR · pith_short_16: 3B4X37YI2ABRP5W4 · pith_short_8: 3B4X37YI

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/3B4X37YI2ABRP5W4PCRG5ZB6MZ \
  | 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: d8797dff08d00317f6dc78a26ee43e6677d7cea230a429ee79048f18bb85b8e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e48f0744f6a947bf8a6d8e93dcca309b943939ddb7dd878714d615925fa8024e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-28T11:42:26Z",
    "title_canon_sha256": "29ed8fa43521feab3c09de371c67d75f96c6205ce216b4eea213a268ae285dc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09080",
    "kind": "arxiv",
    "version": 2
  }
}