Find the beautiful
exception.✳

The difference between
evidence and proof.

Counterseed enumerates every labeled simple undirected graph from one vertex through your chosen bound. A graph is a counterexample when your premise is true and your conclusion is false.

Graphs are examined by vertex count, then edge count, then an explicit binary encoding. The first counterexample is therefore smallest by vertices and, among those, edges. Equivalent relabelings are intentionally retained.

If nothing fails, the claim has survived exactly the declared finite universe. Nothing here proves it for larger graphs.

Real search. Reproducible evidence.

• Exact graph algorithms run in a cancellable Web Worker.
• Expressions use a small typed grammar. No arbitrary code is evaluated.
• Exports include the universe, search order, exact counts, first witness, properties and a noncryptographic enumeration fingerprint.
• The independent Node verifier uses separate graph algorithms to replay your experiment.
• The graph is editable. A single edge can show why the conclusion changes.

Conventions matter.

Graphs have no loops or multiple edges. A single vertex is connected and is a tree. “Eulerian” includes connectedness; the single-vertex graph has an empty Euler walk. Hamiltonian cycles require at least three vertices. Forests have infinite girth; disconnected graphs have infinite diameter.

Original project built for GIBC V2's Open Invention track. Codex assisted with design, code, tests and documentation. No model, account, API key, private dataset or network inference is required.