Pith Number

pith:AOTZMPII

pith:2024:AOTZMPIINRWLRJ46XQ4MHPJU3C

not attested not anchored not stored refs pending

Distribution-flow dependent SDEs driven by (fractional) Brownian motion and Navier-Stokes equations

Michael R\"ockner, Xicheng Zhang, Zimo Hao

arxiv:2405.19034 v2 · 2024-05-29 · 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{AOTZMPIINRWLRJ46XQ4MHPJU3C}

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	2026-07-05T09:49:42.946687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03a7963d086c6cb8a79ebc38c3bd34d8834817a9cfb664150322a33d9a98a8b9

Aliases

arxiv: 2405.19034 · arxiv_version: 2405.19034v2 · doi: 10.48550/arxiv.2405.19034 · pith_short_12: AOTZMPIINRWL · pith_short_16: AOTZMPIINRWLRJ46 · pith_short_8: AOTZMPII

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/AOTZMPIINRWLRJ46XQ4MHPJU3C \
  | 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: 03a7963d086c6cb8a79ebc38c3bd34d8834817a9cfb664150322a33d9a98a8b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30afc53ebce096766eddadb564426a222e05b596612c61d45b147eaecf81f949",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-05-29T12:23:09Z",
    "title_canon_sha256": "221a0e17d52c4912c85ffa47efed5dcd2d5f3b2d991b9e3858657743532cba20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.19034",
    "kind": "arxiv",
    "version": 2
  }
}