Pith Number

pith:VDF33STG

pith:2018:VDF33STGY2PF7ZF3RT2HSF6MMZ

not attested not anchored not stored refs pending

Resolution of Conjectures Related to Lights Out! and Cartesian Products

Bryan Curtis, Bryan Shader, David Livingston, Jonathan Earl

arxiv:1802.05359 v1 · 2018-02-14 · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDF33STGY2PF7ZF3RT2HSF6MMZ}

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	2026-05-18T00:23:15.864458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8cbbdca66c69e5fe4bb8cf47917cc66470619147d019b38df0c947913153b7a

Aliases

arxiv: 1802.05359 · arxiv_version: 1802.05359v1 · doi: 10.48550/arxiv.1802.05359 · pith_short_12: VDF33STGY2PF · pith_short_16: VDF33STGY2PF7ZF3 · pith_short_8: VDF33STG

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/VDF33STGY2PF7ZF3RT2HSF6MMZ \
  | 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: a8cbbdca66c69e5fe4bb8cf47917cc66470619147d019b38df0c947913153b7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9145ba5d4820788cf1f32587813d82365f0c2cd99cfb8400fce90d1e5aac294",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-02-14T23:37:41Z",
    "title_canon_sha256": "7cbf2587b735658266030db5fd0155369cb2b5a13ec6647ea7104d9c27f9afc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.05359",
    "kind": "arxiv",
    "version": 1
  }
}