Pith Number

pith:G27NP27E

pith:2026:G27NP27EJEA5RGI7H57G7W4WI4

not attested not anchored not stored refs pending

Improved Lower Bounds for Proportionally Fair Clustering

Benjamin Cookson, Eva Deltl, Yeeseok Oh

arxiv:2606.07285 v1 · 2026-06-05 · 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{G27NP27EJEA5RGI7H57G7W4WI4}

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	2026-06-08T01:05:17.441539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36bed7ebe44901d8991f3f7e6fdb96473a4808b1f6d432bbde9e9a3218e942fa

Aliases

arxiv: 2606.07285 · arxiv_version: 2606.07285v1 · doi: 10.48550/arxiv.2606.07285 · pith_short_12: G27NP27EJEA5 · pith_short_16: G27NP27EJEA5RGI7 · pith_short_8: G27NP27E

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/G27NP27EJEA5RGI7H57G7W4WI4 \
  | 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: 36bed7ebe44901d8991f3f7e6fdb96473a4808b1f6d432bbde9e9a3218e942fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "321fa37db449352f3d94d7e5434cc2cf921665a2cb5ad21a8c3ade773b2eeb7d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-06-05T13:57:45Z",
    "title_canon_sha256": "a17305148c094e43fc534472fb5648874409324f9eda3df9de3b64e97a533e34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07285",
    "kind": "arxiv",
    "version": 1
  }
}