Pith Number

pith:VHRXCLJZ

pith:2021:VHRXCLJZRYJYJ4BT4NOVCOMTJ7

not attested not anchored not stored refs pending

Efficient Algorithms For Fair Clustering with a New Fairness Notion

Ganesh Ghalme, Narayanan C. Krishnan, Shivam Gupta, Shweta Jain

arxiv:2109.00708 v3 · 2021-09-02 · cs.LG · cs.AI · cs.CY

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VHRXCLJZRYJYJ4BT4NOVCOMTJ7}

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	2026-07-05T05:52:50.307817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9e3712d398e1384f033e35d5139934fcea742e94cad045bdb3f500d08ad8330

Aliases

arxiv: 2109.00708 · arxiv_version: 2109.00708v3 · doi: 10.48550/arxiv.2109.00708 · pith_short_12: VHRXCLJZRYJY · pith_short_16: VHRXCLJZRYJYJ4BT · pith_short_8: VHRXCLJZ

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/VHRXCLJZRYJYJ4BT4NOVCOMTJ7 \
  | 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: a9e3712d398e1384f033e35d5139934fcea742e94cad045bdb3f500d08ad8330

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51c7dd3ec1681742f06703a80e17f22b712ea61f40653234439eb06b152f07d0",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-09-02T04:52:49Z",
    "title_canon_sha256": "5c4f64f54315f94f6156c2152a4cc99e72e414a05c6c7ed02ff5e881c5605ba1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.00708",
    "kind": "arxiv",
    "version": 3
  }
}