Five Possible Centers for a Cube Move of a 10-Realization

Melotti, Ramassamy and Thevenin proposed that a cube move of an alpha-realization, for alpha>1, has at most three possible central points. We give a counterexample at alpha=10: two construction curves with a common focus have at least five distinct intersection points. All foci and boundary vertices of the cube configuration are rational. The proof reduces the intersection equations to a continuous scalar function and certifies five sign changes using rational enclosures of fifth roots. A reflection construction supplies a rational input center and verifies the noncollinearity conditions. The same boundary has at least five output centers for exponents in an open neighborhood of 10. This refutes the three-center bound in Melotti's contribution to Oberwolfach Report 35/2020, p1785, and Remark4.8 of Cube moves for s-embeddings and alpha-realizations (2023), exactly frozen UnsolvedMath record OWR-2654831-006. We do not assert that five is the maximum or that the configuration is a proper embedding; crossed edges are allowed by the source definition. This four-page English preprint includes a standard-library exact arithmetic checker with 67 checks. Developed with AI assistance and self-audited, it is unrefereed, without independent review, proof-assistant verification or absolute-priority certification.