Pith Number

pith:5ZSRZQJ3

pith:2015:5ZSRZQJ34B3KPFMGL34HR5GIAB

not attested not anchored not stored refs pending

Convergence of the $k$-Means Minimization Problem using $\Gamma$-Convergence

Adam M. Johansen, Florian Theil, Matthew Thorpe, Neil Cade

arxiv:1501.01320 v2 · 2015-01-06 · math.ST · math.FA · math.OC · 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{5ZSRZQJ34B3KPFMGL34HR5GIAB}

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	2026-05-18T02:19:42.363794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee651cc13be076a795865ef878f4c8005cf39facbf374238bc0386792ba1628c

Aliases

arxiv: 1501.01320 · arxiv_version: 1501.01320v2 · doi: 10.48550/arxiv.1501.01320 · pith_short_12: 5ZSRZQJ34B3K · pith_short_16: 5ZSRZQJ34B3KPFMG · pith_short_8: 5ZSRZQJ3

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/5ZSRZQJ34B3KPFMGL34HR5GIAB \
  | 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: ee651cc13be076a795865ef878f4c8005cf39facbf374238bc0386792ba1628c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a3f8635e2fa04527841dd1d40019ba6a969b726b6c77705df868569f5fadeef",
    "cross_cats_sorted": [
      "math.FA",
      "math.OC",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2015-01-06T21:19:46Z",
    "title_canon_sha256": "a382c3f8dffff72333a9d6828247409236654412e501c7a93b4c44fd024ff6da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.01320",
    "kind": "arxiv",
    "version": 2
  }
}