Categorical Reformation of Arithmetic and Spacetime Geometry Through Fractal-Adelic Scaffolding

I present Cykloid Influence Theory (CIT) and Recursive Expansive Dynamic Systems (REDS) --- a categorical framework interlacing arithmetic invariants, fractal geometry, and spacetime dynamics through ∞-categories, coalgebraic recursion, and adelic tensor-triangulated structures. By reinterpreting modular arithmetic and spectral number theory via φ-scaled operator algebras and stratified topoi, we resolve classical conjectures (Lehmer, Serre) as stability conditions in recursive geometric flows. This Scaffold reveals gravitational wave echoes and cosmic microwave background (CMB) anomalies as signatures of prime-harmonic resonance in evolving fractal manifolds.