Pith Number

pith:VKLVC3AE

pith:2026:VKLVC3AEEFBZV7QU5QYISTUJZI

not attested not anchored not stored refs pending

On the disjunctive domination numbers of the torus grid graphs

Zhi Qiao

arxiv:2605.19497 v1 · 2026-05-19 · 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{VKLVC3AEEFBZV7QU5QYISTUJZI}

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	2026-05-20T01:05:48.686129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa97516c0421439afe14ec30894e89ca02ef06c933ce7c8dbb2c105116160c03

Aliases

arxiv: 2605.19497 · arxiv_version: 2605.19497v1 · doi: 10.48550/arxiv.2605.19497 · pith_short_12: VKLVC3AEEFBZ · pith_short_16: VKLVC3AEEFBZV7QU · pith_short_8: VKLVC3AE

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/VKLVC3AEEFBZV7QU5QYISTUJZI \
  | 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: aa97516c0421439afe14ec30894e89ca02ef06c933ce7c8dbb2c105116160c03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a342ae6720a612a710c6b0b2c20507295e88caba89711b4c1a079d77ff44ad8b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-19T07:51:05Z",
    "title_canon_sha256": "7e2bebadccd3932d8cf8ca7517cacab51ea3e9fc46635ccce9dcb1316c2f1e80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19497",
    "kind": "arxiv",
    "version": 1
  }
}