The Klimax Torus: The unique aspect ratio whose radii are powers of φ at every scale

A concise result in golden-ratio geometry: It shows that R/r = φ (the golden ratio) is the unique aspect ratio at which a torus's four natural radii — hole, tube, major, and outer rim — form a geometric progression, coming out as four consecutive integer powers of φ. As a consequence, concentric "Klimax" tori stacked so each touches the next produce a gapless chain realizing every consecutive power of φ as a natural radius. Preprint of a paper prepared for submission to The Fibonacci Quarterly.