Symmetry Breaking and Exclusive Duality: Foundations for a Unified Theory of Structures

This paper investigates the logical-mathematical foundations of physical reality, proposing amodel based on the persistence of symmetry breaking from the real to the complex domain.We postulate the existence of two fundamental structures: the Internal Structure S(O)(Hilbert Space/Peano axioms) and the External Structure S(O^-1) (Complex Field). Thetheoretical core lies in the identification of two mutually exclusive regimes: Observation(Real Time φ) and Comprehension (Complex Time ω). We demonstrate that realityresults from a high-frequency oscillation driven by Prime Saturation. The model offers anontological revision of the nature of numbers and motion: natural numbers and rationalsconstitute the discrete building blocks of inertia, while irrational numbers, colliding withthe Planck scale limit, generate the singularities necessary for the "switch" to the complexdimension. Consequently, motion is redefined not as a continuum, but as a stroboscopicregeneration