Pith Number

pith:663HS3A3

pith:2026:663HS3A3BOVLLXMWF5ZVBXRHWM

not attested not anchored not stored refs pending

A combinatorial framework for clustering graph states: Algorithms and hardness for rank-integrity

Blair D. Sullivan, Nathan Claudet, Romain Bourneuf, Rose McCarty, Sang Yoon Kim, St\'ephan Thomass\'e

arxiv:2607.09469 v1 · 2026-07-10 · cs.DS · cs.DM · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{663HS3A3BOVLLXMWF5ZVBXRHWM}

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	2026-07-13T01:20:12.178228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7b6796c1b0baab5dd962f7350de27b3293dd16cb52d082de1e5d5f008cc2ae3

Aliases

arxiv: 2607.09469 · arxiv_version: 2607.09469v1 · doi: 10.48550/arxiv.2607.09469 · pith_short_12: 663HS3A3BOVL · pith_short_16: 663HS3A3BOVLLXMW · pith_short_8: 663HS3A3

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/663HS3A3BOVLLXMWF5ZVBXRHWM \
  | 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: f7b6796c1b0baab5dd962f7350de27b3293dd16cb52d082de1e5d5f008cc2ae3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7baab711d5080de33809d7d309e065b2b2cc20ebc3938839d8f4eb6211c19880",
    "cross_cats_sorted": [
      "cs.DM",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-07-10T14:42:55Z",
    "title_canon_sha256": "d2bc51fc464c0fba847c1af74ff4e2fbcc751580f76737d17af35d29e798e018"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.09469",
    "kind": "arxiv",
    "version": 1
  }
}