Unique Paths

Invariant: When cell (r,c) is processed, every predecessor state already meets its definition; the new state aggregates every legal way to enter the cell exactly as required.

candidate confidence: 0.555 · metadata_only

Invariant: Every valid outcome maps to one counting representation, or to a known fixed multiplicity that is explicitly corrected.

candidate confidence: 0.665 · metadata_only

Invariant: After processing i, every state through i equals the true value under its definition, and every future transition reads only these finalized states.

candidate confidence: 0.470 · metadata_only