Topological protection of the Mirny axis: why local isotropy cannot be refuted locally

Note No. 2 predicted a global, distinguished winding axis of the toroidal universe; the reviewer raises the standard objection: the distinguished direction violates Lorentz invariance. It is shown here: (i) the Mirny axis is not a geometric direction, but an element of the fundamental group of the torus, pi1(T2) = Z2, whose carriers are two independent cycles — meridian and longitude; (ii) the local neighborhood of any observer is topologically contractible (ball, pi1 = 0), therefore, no local experiment — an interferometer, a pendulum, a measurement of the speed of light — can neither see the axis nor refute it; (iii) isolation is required only for global correlations, which removes the conflict with local isotropy without violating Lorentz invariance; (iv) topological protection does not depend on the dynamics of the medium and undergoes a revision of its parameters; however, protection explains the survival of structure, not its observability — falsifier No. 2 remains in force.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-26
DOI
https://doi.org/10.5281/zenodo.23672531
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

Topological protection of the Mirny axis: why local isotropy cannot be refuted locally

Borodin Oleg BORODIN O.A.
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

Topological protection of the Mirny axis: why local isotropy cannot be refuted locally

Borodin Oleg BORODIN O.A.
preprint en

Abstract

Note No. 2 predicted a global, distinguished winding axis of the toroidal universe; the reviewer raises the standard objection: the distinguished direction violates Lorentz invariance. It is shown here: (i) the Mirny axis is not a geometric direction, but an element of the fundamental group of the torus, pi1(T2) = Z2, whose carriers are two independent cycles — meridian and longitude; (ii) the local neighborhood of any observer is topologically contractible (ball, pi1 = 0), therefore, no local experiment — an interferometer, a pendulum, a measurement of the speed of light — can neither see the axis nor refute it; (iii) isolation is required only for global correlations, which removes the conflict with local isotropy without violating Lorentz invariance; (iv) topological protection does not depend on the dynamics of the medium and undergoes a revision of its parameters; however, protection explains the survival of structure, not its observability — falsifier No. 2 remains in force.

Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
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Topological protection of the Mirny axis: why local isotropy cannot be refuted locally — Borodin Oleg BORODIN O.A. · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS