Pith Number

pith:5FEUYZG3

pith:2026:5FEUYZG3ZGFCYXDHU32XI3V7RC

not attested not anchored not stored refs pending

Mean-Field Stochastic PDEs: Well-posedness and Quantitative Dimension-Free Propagation of Chaos

Luhan Yang, Wei Hong, Wei Liu

arxiv:2607.17195 v1 · 2026-07-19 · 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{5FEUYZG3ZGFCYXDHU32XI3V7RC}

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	2026-07-21T01:21:20.411542Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9494c64dbc98a2c5c67a6f5746ebf88a3df85c156da1e4d6f19aff87b2fb979

Aliases

arxiv: 2607.17195 · arxiv_version: 2607.17195v1 · doi: 10.48550/arxiv.2607.17195 · pith_short_12: 5FEUYZG3ZGFC · pith_short_16: 5FEUYZG3ZGFCYXDH · pith_short_8: 5FEUYZG3

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/5FEUYZG3ZGFCYXDHU32XI3V7RC \
  | 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: e9494c64dbc98a2c5c67a6f5746ebf88a3df85c156da1e4d6f19aff87b2fb979

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b9085fea4fc6d3dbc4868d5e4cacffd30e40f4e922730fbf5ecff71755fb42a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-19T11:18:31Z",
    "title_canon_sha256": "e377b682d95797f2e3bda9108050ec5958e9c921752bff56e2e3cf0ebf27397d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17195",
    "kind": "arxiv",
    "version": 1
  }
}