Pith Number

pith:VXKOGQ4L

pith:2026:VXKOGQ4LTVHG23BGJWYR7RBYJS

not attested not anchored not stored refs pending

Many holes but no large one: maximizing $k$-holes while forbidding $(k+1)$-holes

Adam D\v{z}avoronok, Aleksa D\v{z}uklevski, Alica Dom\'anyov\'a, Martin Andri\v{c}\'ik, Matou\v{s} \v{S}afr\'anek

arxiv:2606.08762 v1 · 2026-06-07 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VXKOGQ4LTVHG23BGJWYR7RBYJS}

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	2026-06-09T02:07:37.947642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

add4e3438b9d4e6d6c264db11fc4384caa8ebed77e79e12da7ccbd19383ae4e4

Aliases

arxiv: 2606.08762 · arxiv_version: 2606.08762v1 · doi: 10.48550/arxiv.2606.08762 · pith_short_12: VXKOGQ4LTVHG · pith_short_16: VXKOGQ4LTVHG23BG · pith_short_8: VXKOGQ4L

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/VXKOGQ4LTVHG23BGJWYR7RBYJS \
  | 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: add4e3438b9d4e6d6c264db11fc4384caa8ebed77e79e12da7ccbd19383ae4e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3bdd1aacdd384856cbcf770561d11e2dbc7a75ebc994d7da05f39d60dedcc50",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-07T18:02:36Z",
    "title_canon_sha256": "8be68e3664f8fbeb0f84fe9c0b9072d6a2e6d5c903f2baaae3a4cf98e8dcaf68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08762",
    "kind": "arxiv",
    "version": 1
  }
}