Pith Number

pith:2CFZH2AC

pith:2023:2CFZH2ACBXEGKHSZVVBFFBHFSP

not attested not anchored not stored refs pending

Second order fractional mean-field SDEs with singular kernels and measure initial data

Michael R\"ockner, Xicheng Zhang, Zimo Hao

arxiv:2302.04392 v2 · 2023-02-09 · math.AP · 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{2CFZH2ACBXEGKHSZVVBFFBHFSP}

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.

Cited by

2 papers in Pith

Kinetic Theory with Fluctuations: Strong Well-Posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki System

On some topological and spectral properties of kinetic Langevin processes driven by L{\'e}vy noises

Receipt and verification

First computed	2026-07-05T05:50:13.234797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d08b93e8020dc8651e59ad425284e593c36fe667fb009817ef45ff4de59695c9

Aliases

arxiv: 2302.04392 · arxiv_version: 2302.04392v2 · doi: 10.48550/arxiv.2302.04392 · pith_short_12: 2CFZH2ACBXEG · pith_short_16: 2CFZH2ACBXEGKHSZ · pith_short_8: 2CFZH2AC

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/2CFZH2ACBXEGKHSZVVBFFBHFSP \
  | 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: d08b93e8020dc8651e59ad425284e593c36fe667fb009817ef45ff4de59695c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "625544559df054ba781ce76ad8319eb6f9e242f91ce2708b155ec5c989ecf76c",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-02-09T01:13:53Z",
    "title_canon_sha256": "da35909729256158eab92f33976e1b448baea1d0270170e0f71da241219c5fd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2302.04392",
    "kind": "arxiv",
    "version": 2
  }
}