Pith Number

pith:7BR3IXLH

pith:2025:7BR3IXLHSV2MWV5P7EOFDBUOF6

not attested not anchored not stored refs pending

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations

Huaxiang L\"u, Michael R\"ockner, Xiangchan Zhu

arxiv:2504.16687 v2 · 2025-04-23 · math.AP · math-ph · math.MP · 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{7BR3IXLHSV2MWV5P7EOFDBUOF6}

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

1 paper in Pith

Non-Uniqueness for Nonlinear Fokker--Planck Equations and Their Associated Distribution-Dependent SDEs

Receipt and verification

First computed	2026-07-05T10:56:17.805750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f863b45d679574cb57aff91c51868e2fa71e84fad0f9d53f5521103e25f426e3

Aliases

arxiv: 2504.16687 · arxiv_version: 2504.16687v2 · doi: 10.48550/arxiv.2504.16687 · pith_short_12: 7BR3IXLHSV2M · pith_short_16: 7BR3IXLHSV2MWV5P · pith_short_8: 7BR3IXLH

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/7BR3IXLHSV2MWV5P7EOFDBUOF6 \
  | 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: f863b45d679574cb57aff91c51868e2fa71e84fad0f9d53f5521103e25f426e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b02a4018fb64328dd19067a7c4df32147e40e9196b3e453204093fed23a06e6",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-04-23T13:16:04Z",
    "title_canon_sha256": "dbdd3e169a21ff5966eb23ae1f96cc9e9b3edeaf0dbc5f035de5c77e6b106275"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.16687",
    "kind": "arxiv",
    "version": 2
  }
}