Mirny's Cosmodynamics: Notes. Note No. 3 Rational loops — subsets: why circle searchers don't find them by construction

In the picture of a toroidal universe (preprint DOI: 10.5281/zenodo.23039759), the dominant geodesics have an irrational slope and do not close; rational loops form a subset of measure zero. It is shown here: (i) a tabletop experiment — the lines of force of a magnet — reproduces the same hierarchy: the near lines are almost circles, the far ones are elongated spirals; (ii) a geodesic on a torus with a rational slope of m/n closes after n turns, with an irrational one it never closes; (iii) zero result of searches for matching circles (Cornish–Spergel, WMAP, Planck) in this picture, it is not the absence of a topology, but its direct prediction; (iv) a prediction about weak pairs with a small offset along the selected slopes is formulated and a falsifier is assigned.