Pith Number

pith:663YMHJA

pith:2019:663YMHJAZDVQ5ABMMYPRTZ4ZF4

not attested not anchored not stored refs pending

A Mean Field Games approach to Cluster Analysis

Fabio Camilli, Laura Aquilanti, Raul De Maio, Simone Cacace

arxiv:1907.02261 v2 · 2019-07-04 · math.NA · cs.NA · 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{663YMHJAZDVQ5ABMMYPRTZ4ZF4}

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	2026-07-05T00:27:58.046622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7b7861d20c8eb0e802c661f19e7992f1351f64b1edc91c641533ee092c61d77

Aliases

arxiv: 1907.02261 · arxiv_version: 1907.02261v2 · doi: 10.48550/arxiv.1907.02261 · pith_short_12: 663YMHJAZDVQ · pith_short_16: 663YMHJAZDVQ5ABM · pith_short_8: 663YMHJA

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/663YMHJAZDVQ5ABMMYPRTZ4ZF4 \
  | 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: f7b7861d20c8eb0e802c661f19e7992f1351f64b1edc91c641533ee092c61d77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce507df923602cee02582151af26a66e9ff1a81e61fc37c0ff7842a724545ba8",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-07-04T07:57:52Z",
    "title_canon_sha256": "3fbd98113f16127e98ca6c022a2c0327e3f1a805841cd27777854aba8fc7eef6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.02261",
    "kind": "arxiv",
    "version": 2
  }
}