Pith Number

pith:PAAGRIFE

pith:2013:PAAGRIFEDPZE7FRHNCEO25JPHY

not attested not anchored not stored refs pending

Strong Consistency of Factorial K-means Clustering

Yoshikazu Terada

arxiv:1301.0676 v5 · 2013-01-04 · 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{PAAGRIFEDPZE7FRHNCEO25JPHY}

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	2026-05-18T02:59:08.821024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

780068a0a41bf24f96276888ed752f3e12e18cff150ed232e894d6ba0456c95d

Aliases

arxiv: 1301.0676 · arxiv_version: 1301.0676v5 · doi: 10.48550/arxiv.1301.0676 · pith_short_12: PAAGRIFEDPZE · pith_short_16: PAAGRIFEDPZE7FRH · pith_short_8: PAAGRIFE

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/PAAGRIFEDPZE7FRHNCEO25JPHY \
  | 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: 780068a0a41bf24f96276888ed752f3e12e18cff150ed232e894d6ba0456c95d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64d731435680db5e392af34b9b61b969eee8c1a0460e9bfbac489070efbd614a",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-01-04T05:55:48Z",
    "title_canon_sha256": "5b40030dea4d0af5167f7b7c262d5136f324500312aad8bc1ff8be474d876b62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0676",
    "kind": "arxiv",
    "version": 5
  }
}