The Relativistic Rose: Temporal Dilation as Geometry of Squares 1·3·5·7

A geometric construction using four concentric squares with sides in proportions 1, 3, 5, 7 rotating at inversely proportional angular velocities reveals spontaneous emergence of relativistic time dilation, galactic spiral morphology, and toroidal topology. The invariant r×ω=constant governs all scales. No algebraic formalism is assumed — the geometry precedes and contains it. We present a minimal geometric construction — four concentric squares with half-sides 1, 3, 5, 7 (the gnomon numbers) rotating at inversely proportional angular velocities — governed by the conservation law r×ω=constant. This single constraint produces, without algebraic assumption, the formal structure of special relativistic time dilation: an observer co-rotating with the inner square (r=1, ω=7) completes seven cycles while an observer on the outer square (r=7, ω=1) completes one. The intersection points of the rotating square contours with four equidistant rays trace a closed periodic surface we call the Relativistic Rose. This surface reproduces the morphology of galactic spiral arms — a consequence, not an analogy, of the same differential rotation law observed in the Milky Way. Extended to three dimensions with seven levels per axis, the construction generates the Z₇³ toroidal lattice. We propose that known mathematics — from Euclidean geometry to relativity to topology — represents distinct cross-sections of a single geometric membrane, of which the Relativistic Rose is the minimal