Pith Number

pith:3ODJVRGT

pith:2024:3ODJVRGTOVR6PD5UNZJXHQACAY

not attested not anchored not stored refs pending

Wasserstein $k$-Centers Clustering for Distributional Data

Masaaki Imaizumi, Ryo Okano

arxiv:2407.08228 v4 · 2024-07-11 · stat.ME

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3ODJVRGTOVR6PD5UNZJXHQACAY}

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	2026-07-05T11:25:02.665573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db869ac4d37563e78fb46e5373c002061b9da6f20886346cfe1279ba4fd316e2

Aliases

arxiv: 2407.08228 · arxiv_version: 2407.08228v4 · doi: 10.48550/arxiv.2407.08228 · pith_short_12: 3ODJVRGTOVR6 · pith_short_16: 3ODJVRGTOVR6PD5U · pith_short_8: 3ODJVRGT

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/3ODJVRGTOVR6PD5UNZJXHQACAY \
  | 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: db869ac4d37563e78fb46e5373c002061b9da6f20886346cfe1279ba4fd316e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e66b4aa6a6cd9626f5e95ce36d693b4668a18b5387e328aac0495e0d40a0d459",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2024-07-11T07:03:42Z",
    "title_canon_sha256": "89fee292293640d185dad0fc2d5a2000cb3cf40f0c93ecc31b4d169d18e3ef59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.08228",
    "kind": "arxiv",
    "version": 4
  }
}