Pith Number

pith:QNFOPPNC

pith:2012:QNFOPPNCR35D2IQ3YLS4LEQU7M

not attested not anchored not stored refs pending

Strong Consistency of Reduced K-means Clustering

Yoshikazu Terada

arxiv:1212.4942 v4 · 2012-12-20 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QNFOPPNCR35D2IQ3YLS4LEQU7M}

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	2026-05-18T02:59:08.835017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

834ae7bda28efa3d221bc2e5c59214fb2678cd025a2b9968a01cd9b18717b332

Aliases

arxiv: 1212.4942 · arxiv_version: 1212.4942v4 · doi: 10.48550/arxiv.1212.4942 · pith_short_12: QNFOPPNCR35D · pith_short_16: QNFOPPNCR35D2IQ3 · pith_short_8: QNFOPPNC

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/QNFOPPNCR35D2IQ3YLS4LEQU7M \
  | 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: 834ae7bda28efa3d221bc2e5c59214fb2678cd025a2b9968a01cd9b18717b332

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e20972775f445a2b0f1415e828b0ab280977af20469d13e507f6a559a72ce7ad",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2012-12-20T07:46:35Z",
    "title_canon_sha256": "a53e1ea4bd5fbb93c07bf3afbd1c716b996a2402069a6bab65df2cc5a5c9343f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4942",
    "kind": "arxiv",
    "version": 4
  }
}