Pith Number

pith:VJM4I32X

pith:2026:VJM4I32XQN7Y3LS75NR4N52ZB2

not attested not anchored not stored refs pending

The minimum degree question for the Maker Breaker Domination Game

Georg Grasegger, Jakob F\"uhrer, Oliver Roche-Newton, Paul Hametner

arxiv:2606.04824 v1 · 2026-06-03 · 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{VJM4I32XQN7Y3LS75NR4N52ZB2}

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	2026-06-04T01:09:31.324747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa59c46f57837f8dae5feb63c6f7590ea9ebf570074fbc884314227d0a3b21fe

Aliases

arxiv: 2606.04824 · arxiv_version: 2606.04824v1 · doi: 10.48550/arxiv.2606.04824 · pith_short_12: VJM4I32XQN7Y · pith_short_16: VJM4I32XQN7Y3LS7 · pith_short_8: VJM4I32X

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/VJM4I32XQN7Y3LS75NR4N52ZB2 \
  | 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: aa59c46f57837f8dae5feb63c6f7590ea9ebf570074fbc884314227d0a3b21fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5169679509ec66376b912bea27b8d7d954587ee0990e63779cbe1e0cf2104ba1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-03T12:46:11Z",
    "title_canon_sha256": "b364612377e8c33763cdce0a8f424e42fb693ffa4757e2f563d2305f4bc71ba0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.04824",
    "kind": "arxiv",
    "version": 1
  }
}