Pith Number

pith:FKWE3GV5

pith:2017:FKWE3GV5WJ6MQMAZ2BLJ4DAFFF

not attested not anchored not stored refs pending

Weak order in averaging principle for stochastic wave equations with a fast oscillation

Hongbo Fu, Jicheng Liu, Li Wan, Xianming Liu

arxiv:1701.07984 v1 · 2017-01-27 · 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{FKWE3GV5WJ6MQMAZ2BLJ4DAFFF}

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	2026-05-18T00:48:29.325680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2aac4d9abdb27cc83019d0569e0c052958d334d445d14fc852b709803d525908

Aliases

arxiv: 1701.07984 · arxiv_version: 1701.07984v1 · doi: 10.48550/arxiv.1701.07984 · pith_short_12: FKWE3GV5WJ6M · pith_short_16: FKWE3GV5WJ6MQMAZ · pith_short_8: FKWE3GV5

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/FKWE3GV5WJ6MQMAZ2BLJ4DAFFF \
  | 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: 2aac4d9abdb27cc83019d0569e0c052958d334d445d14fc852b709803d525908

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8447dddd933fec61ee4ce13a2a264638546c616c0045544903fc0ee86279fa01",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-01-27T09:37:21Z",
    "title_canon_sha256": "009e6cfc1d79eb82f4035e029bb1680dfdb8a6ccafad11bedd881a8636afe2a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.07984",
    "kind": "arxiv",
    "version": 1
  }
}