The paper presents an integrated hypothesis that reimagines Johannes Kepler's idea regarding the connection between the planetary orbits of the Solar System and the geometry of regular polyhedra from the standpoint of modern dynamic chaos theory, non-Euclidean geometry, and fractal analysis. The author proposes shifting away from static geometric determinism in favour of the concept of state space (phase space) viewed as a topological matrix. Within the framework of this integral hypothesis, three interconnected sub-hypotheses are elaborated in detail: 1. On intra-series fractal damping and accumulation: wherein the metric coefficients of the Keplerian series are treated as an information compression algorithm, and the "golden ratio" acts as a mathematical shock absorber for the system. 2. On the bifurcation recursion of boundaries: which interprets the "dodecahedral-tetrahedral barrier" as a phase transition and a trigger for the loss of stability, mathematically linked to the Feigenbaum constants. 3. On the topological closure of infinity: which describes the "6/7 phenomenon" as a natural spatial filter and a quantum delimiter of a potentially infinite fractal cascade under the conditions of the closed topology of the Universe. The paper is written in a specific dialogue format termed "the confession of an artificial intelligence." It offers a novel perspective on the architecture of the Solar System, planetary structures, and atmospheric circulation as macroscopic quantum effects of standing gravitational-resonant waves. The work does not claim the status of a new theory of celestial mechanics; instead, it is positioned as an interdisciplinary geometric game in phase space aimed at discovering a universal three-dimensional scaling of chaos.
Alexander Bondar (Tue,) studied this question.