Pith Number

pith:BIBJ4AM6

pith:2026:BIBJ4AM6TL2ZA24UYAFRRTMWA6

not attested not anchored not stored refs pending

Quantitative Propagation of Chaos and Fluctuations for Kinetic McKean--Vlasov SDEs with Singular Interaction Kernels

Xianliang Zhao, Xicheng Zhang, Zimo Hao

arxiv:2607.13379 v1 · 2026-07-15 · math.PR · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BIBJ4AM6TL2ZA24UYAFRRTMWA6}

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	2026-07-16T00:22:14.884490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a029e019e9af5906b94c00b18cd96078073fceb8444bdd7d059e3bb4554e73b

Aliases

arxiv: 2607.13379 · arxiv_version: 2607.13379v1 · doi: 10.48550/arxiv.2607.13379 · pith_short_12: BIBJ4AM6TL2Z · pith_short_16: BIBJ4AM6TL2ZA24U · pith_short_8: BIBJ4AM6

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/BIBJ4AM6TL2ZA24UYAFRRTMWA6 \
  | 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: 0a029e019e9af5906b94c00b18cd96078073fceb8444bdd7d059e3bb4554e73b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19348209955ec43fc8a4854941b163a0770623d135e32c1131a013a1bcfa0e8d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-15T02:18:01Z",
    "title_canon_sha256": "eb83efee35e634aa762cdaebc0bb0fb24337a12d68d9e8c21763c2f7ba652b06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13379",
    "kind": "arxiv",
    "version": 1
  }
}