Pith Number

pith:Q7HSCOIT

pith:2010:Q7HSCOITOIVZSSW27UPM4IS5HD

not attested not anchored not stored refs pending

Stochastic Mean-Field Limit: Non-Lipschitz Forces \& Swarming

Fran\c{c}ois Bolley (CEREMADE), Jos\'e Alfredo Ca\~nizo, Jos\'e Antonio Carrillo

arxiv:1009.5166 v2 · 2010-09-27 · 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{Q7HSCOITOIVZSSW27UPM4IS5HD}

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	2026-05-18T04:04:53.527110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87cf213913722b994adafd1ece225d38c92d26fc30425577c718d892198d2657

Aliases

arxiv: 1009.5166 · arxiv_version: 1009.5166v2 · doi: 10.48550/arxiv.1009.5166 · pith_short_12: Q7HSCOITOIVZ · pith_short_16: Q7HSCOITOIVZSSW2 · pith_short_8: Q7HSCOIT

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/Q7HSCOITOIVZSSW27UPM4IS5HD \
  | 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: 87cf213913722b994adafd1ece225d38c92d26fc30425577c718d892198d2657

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "662ceab1377d8bab7ea40a19325cf2b6f8ce8d768ac7648a50fc4df051f3c03f",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-09-27T06:21:14Z",
    "title_canon_sha256": "266c69a9f6ba6540c602b1c58d525dacfa4a5024d1433008747b35c70738ed48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5166",
    "kind": "arxiv",
    "version": 2
  }
}