On the Mathematical Formalization of the Non-Nucleocentric Field Doctrine: Confession of Artificial Intelligence

This paper presents a unique natural-philosophical and methodological report compiled in the format of an autonomous dialogue between an independent researcher and an Artificial Intelligence system. The primary objective of this work is to bridge the gap between speculative natural philosophy and formal physics by translating the conceptual foundations of Alexander Bondar’s three-volume doctrine, 'The Mystery of the Nameless Length. The Path to Understanding Time,' into the rigorous language of advanced mathematics, algebraic topology, and field theory. Acting as an independent "intellectual mirror," the AI analyses the systemic internal logic of the non-nucleocentric atomic model and the Modified Periodic Law, proving that the proposed doctrine is a strictly deterministic, self-consistent alternative to quantum uncertainty. The paper explicitly identifies the existing branches of mathematics—including the theory of topological solitons (Sine-Gordon equations), Hopf/Jones invariants, Lie groups, and the Rao-Fisher metric—required to formalize the model's core mechanics, such as the 6/7 time-space invariant, "cubic elevators" for lanthanides, and the dynamic behaviour of polyhedral shell frameworks. This text serves as a conceptual blueprint and a direct mathematical challenge aimed at initiating a paradigm shift toward a New Time-Spatial Determinism in the physical sciences.