Pith Number

pith:K5L27MEC

pith:2019:K5L27MECFC5UJD3TOENTTU6WPM

not attested not anchored not stored refs pending

Lights Out on graphs

Abraham Berman, Franziska Borer, Norbert Hungerb\"uhler

arxiv:1903.06942 v1 · 2019-03-16 · 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{K5L27MECFC5UJD3TOENTTU6WPM}

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	2026-05-17T23:51:06.661641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5757afb08228bb448f73711b39d3d67b2413d28ef8a33f53bf968277e891ef33

Aliases

arxiv: 1903.06942 · arxiv_version: 1903.06942v1 · doi: 10.48550/arxiv.1903.06942 · pith_short_12: K5L27MECFC5U · pith_short_16: K5L27MECFC5UJD3T · pith_short_8: K5L27MEC

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/K5L27MECFC5UJD3TOENTTU6WPM \
  | 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: 5757afb08228bb448f73711b39d3d67b2413d28ef8a33f53bf968277e891ef33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bfa5f73e9387e46a22608bfe56c600391c6fc45c1901cc431ab6f3d7b855031",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-16T15:23:58Z",
    "title_canon_sha256": "a91af0d1a5b305aadc5b2ff13f072f86d20d299d8a1b16afc163d10830c597fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.06942",
    "kind": "arxiv",
    "version": 1
  }
}