Pith Number

pith:TJN2TP4B

pith:2013:TJN2TP4BEQYIKJRJQVVUEDOBFZ

not attested not anchored not stored refs pending

A balanced k-means algorithm for weighted point sets

Andreas Brieden, Peter Gritzmann, Steffen Borgwardt

arxiv:1308.4004 v2 · 2013-08-19 · math.OC · 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{TJN2TP4BEQYIKJRJQVVUEDOBFZ}

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	2026-05-18T01:10:00.291926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a5ba9bf812430852629856b420dc12e61f560fe23d96a4e8510d1098ff076fd

Aliases

arxiv: 1308.4004 · arxiv_version: 1308.4004v2 · doi: 10.48550/arxiv.1308.4004 · pith_short_12: TJN2TP4BEQYI · pith_short_16: TJN2TP4BEQYIKJRJ · pith_short_8: TJN2TP4B

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/TJN2TP4BEQYIKJRJQVVUEDOBFZ \
  | 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: 9a5ba9bf812430852629856b420dc12e61f560fe23d96a4e8510d1098ff076fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3dd39eb0f81c96ce42da961957aa29c2685dbe31233dd94263cd80292592acf6",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-08-19T12:46:33Z",
    "title_canon_sha256": "340237347be3f77a03db7469d817f46013be4d4f220f6ed7f4024cb48f5b199b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4004",
    "kind": "arxiv",
    "version": 2
  }
}