A two-cube cubulation of the AIM free-by-cyclic example

We construct a finite locally CAT(0) unit cube complex with one vertex, seven edges, eight squares, and two three-dimensional cubes, with fundamental group the mapping torus of a to a, b to ab, and c to bcb. Its universal cover gives a free proper cocompact cubical action of the exact group in AIM Question 5.2. The positive final b is essential. Complete attaching data, signed links, and reversible group identifications are supplied. The note also explains a qualitative existence deduction using earlier WPD, Morse, finite-completion, and gluing results, with the group-specific hypotheses checked. The explicit small finite model is the concrete contribution. No historical firstness, absolute novelty, minimality, or virtual specialness claim is made. The deposit includes the research note, standalone LaTeX source, and a dependency-free Python verification package with optimization-safe checks, clean output regeneration, integrity pins, and corruption controls. Finite computations supplement the written proof. Extensive AI tools were used in discovery, drafting, and internal independent adversarial review. This is unrefereed research, with no external human peer review or proof-assistant certification.