Mirny's Cosmodynamics: Notes. Note No. 3 Rational loops — subsets: why circle searchers don't find them by construction
Abstract
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.
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BibTeX
@misc{borodin2026mirnys,
title = {{Mirny's Cosmodynamics: Notes. Note No. 3 Rational loops — subsets: why circle searchers don't find them by construction}},
author = {Oleg Borodin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23649626},
url = {https://zenodo.org/records/23649626},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mirny's Cosmodynamics: Notes. Note No. 3 Rational loops — subsets: why circle searchers don't find them by construction
AU - Oleg Borodin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23649626
UR - https://zenodo.org/records/23649626
AB - 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.
ER -