Dual Series Structure in Unified Geometric Theory: Frequency Cascade and Reactive Amplitude Expansion

This paper formulates a core component of unified geometric theory by introducing two interlinked series structures: the frequency cascade νₙ=ν · (1/2)ⁿ, and the amplitude series φₙ = A · (i/ω)ⁿ. The frequency series represents the hierarchical subdivision of fundamental curvature modes, while the amplitude series models the recursive, damped, and rotated propagation of fields. Together, these series explain field confinement, wave interference, and attenuation across spatial scales. This framework unifies electromagnetic, gravitational, and matter behavior through a single geometric origin: the structured propagation of closed surface deformation. Author: Tetsuo Konno https://orcid.org/0009-0002-1842-7865