Pith Number

pith:N6WDJADK

pith:2020:N6WDJADKQLUTLNQ33IQVI6N4YS

not attested not anchored not stored refs pending

Selecting the Number of Clusters $K$ with a Stability Trade-off: an Internal Validation Criterion

Alex Mourer, Florent Forest, Hanane Azzag, J\'er\^ome Lacaille, Mustapha Lebbah

arxiv:2006.08530 v3 · 2020-06-15 · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N6WDJADKQLUTLNQ33IQVI6N4YS}

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	2026-07-05T06:10:50.627649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fac34806a82e935b61bda215479bcc4bf170513c05db82fa902a6d34d2c63e9

Aliases

arxiv: 2006.08530 · arxiv_version: 2006.08530v3 · doi: 10.48550/arxiv.2006.08530 · pith_short_12: N6WDJADKQLUT · pith_short_16: N6WDJADKQLUTLNQ3 · pith_short_8: N6WDJADK

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/N6WDJADKQLUTLNQ33IQVI6N4YS \
  | 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: 6fac34806a82e935b61bda215479bcc4bf170513c05db82fa902a6d34d2c63e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "712146091091fee26564ed68018c249d47ab989dab925465af53256a1d152ee9",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2020-06-15T16:38:48Z",
    "title_canon_sha256": "86ac11caf53d4f3d54bfb77e0e5b33ca375e6a0f381bcf90613f9c96b698c348"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.08530",
    "kind": "arxiv",
    "version": 3
  }
}