Pith Number

pith:JYBFZ342

pith:2026:JYBFZ342AUNGYCHTLTKY4PUWBT

not attested not anchored not stored refs pending

Check, Please: Verifiably Fair Clustering

Edith Elkind, Jeremy Vollen, Yu He

A new fairness notion for clustering can be checked efficiently while approximating full proportional representation guarantees.

arxiv:2605.12317 v2 · 2026-05-12 · cs.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JYBFZ342AUNGYCHTLTKY4PUWBT}

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.

Claims

C1strongest claim

We introduce Default Coalitions mPJR+ (DC-mPJR+): a new proportionality concept that offers representation guarantees to a restricted set of coalitions around unselected centers, and as a result, admits an O(mn log n + mnk) verification algorithm. DC-mPJR+ is satisfied by SEAR and any solution satisfying γ-DC-mPJR+ also satisfies (γ + 2)-mPJR+.

C2weakest assumption

That the restriction to default coalitions around unselected centers provides a sufficient proxy for global fairness, as captured by the (γ + 2) approximation guarantee to mPJR; this appears in the abstract's description of the relationship between DC-mPJR+ and mPJR.

C3one line summary

DC-mPJR+ is a new proportionality concept for clustering that can be verified in O(mn log n + mnk) time and ensures that any clustering satisfying it also satisfies an approximate version of the stronger mPJR fairness property.

Receipt and verification

First computed	2026-05-28T01:04:08.728114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e025cef9a051a6c08f35cd58e3e960cc10348e4caf331b95ba83cd3950f09c6

Aliases

arxiv: 2605.12317 · arxiv_version: 2605.12317v2 · doi: 10.48550/arxiv.2605.12317 · pith_short_12: JYBFZ342AUNG · pith_short_16: JYBFZ342AUNGYCHT · pith_short_8: JYBFZ342

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/JYBFZ342AUNGYCHTLTKY4PUWBT \
  | 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: 4e025cef9a051a6c08f35cd58e3e960cc10348e4caf331b95ba83cd3950f09c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d54825e499e9d6ebc154a33511e00b13ccdf9630da927ba739f218c53e1859f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-05-12T16:02:24Z",
    "title_canon_sha256": "7d242be1b6b1f3570677d14f1de4a0fc08e6444b1692711e0a03a35cde45cb2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12317",
    "kind": "arxiv",
    "version": 2
  }
}