Pith Number

pith:CK4W5AT6

pith:2016:CK4W5AT6N4NO33OTG4XNI4WO3V

not attested not anchored not stored refs pending

Ergodicity and propagation of chaos for mean field kinetic particles

Pierre Monmarch\'e

arxiv:1603.03179 v4 · 2016-03-10 · 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{CK4W5AT6N4NO33OTG4XNI4WO3V}

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	2026-05-18T00:35:48.951453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12b96e827e6f1aededd3372ed472cedd4af81b416f415c54ecec07bb81da1677

Aliases

arxiv: 1603.03179 · arxiv_version: 1603.03179v4 · doi: 10.48550/arxiv.1603.03179 · pith_short_12: CK4W5AT6N4NO · pith_short_16: CK4W5AT6N4NO33OT · pith_short_8: CK4W5AT6

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/CK4W5AT6N4NO33OTG4XNI4WO3V \
  | 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: 12b96e827e6f1aededd3372ed472cedd4af81b416f415c54ecec07bb81da1677

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "949990a77f99ee9959326e9a64dc97cf11368e5a0f530a90875a64ece72d2257",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-03-10T08:15:58Z",
    "title_canon_sha256": "a3f55152c159b3c6480f91ac3b583dd886a4fb9b9c6190f9cd9a167cf31a10dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.03179",
    "kind": "arxiv",
    "version": 4
  }
}