The Toroidal Matruška Atom Model: Topological Mechanics under Temporal Discretization and Relativistic Constraints

This study presents a comprehensive refinement of the Toroidal Matruška Atom Model and proposes a mathematical and topological connection between cosmic-scale boundaries and microphysical systems. Under the axiom of temporal discretization, space-time is modeled as a discrete stack of Time Plates, each with a thickness of one Planck length (ℓₚ). Mass accumulation is described by a reverse-engineered accumulation integral, which is proposed to transform a neutrino baseline wave envelope with an energy of 1.82 eV into a stable Ergunon (ε) segment with an energy of 0.511 MeV. The proton is modeled as a closed topological string comprising 1836 Ergunons, subject to relativistic compression and dual-axis rotational-spin constraints. In addition, probability distributions are reinterpreted as a multilayer mechanical “basket-weave” configuration governed by a 1, 3, 5, 7 shell symmetry. The framework is used to formulate numerical thresholds associated with the hydrogen ionization energy (13.6 eV), the free-neutron lifetime (approximately 880 s), and the beta-decay energy release (0.782 MeV). Finally, radioactive instability and transuranic limits, including the proposed uranium threshold, are interpreted through a geometrical failure function (Ω), attributed to the inability of a finite Ergunon chain to achieve smooth 360-degree phase closure across expanding Matruška radii. Keywords: Toroidal Atom Model; Time Plate; Ergunon Segment; Basket-Weave Lattice; Topological Closure Failure; Relativistic Deformation.