The Frequency Architecture of the Periodic Table: A Bottom-Up Structural Lattice Model under the IMS Framework

Abstract—This paper outlines a complete, self-consistent restructuring of physical chemistry and nuclear structure under the strict rules of the Infinite Mass Shuffling (IMS) Model. Discarding the abstract four-dimensional spacetime continuum, dark matter, and dark energy, we demonstrate that physical reality emerges exclusively from the geometric phase-locking, frequency modulation, and structural folding of localized single-phase wave states operating within an absolute, propertyless void. We formalize the exact mathematical progression of a proton as a 66-generation fractal wave vault containing exactly 442 quintillion solitons, map the internal quark node line precisely to Layer 22, and derive the quadratic scaling rules (2n²) of the outer electron atmosphere. Finally, we establish the Nuclear Nesting Law, proving that the entire periodic table builds itself on a scale-invariant basis by repeating and nesting a primordial, three-dimensional Helium-4 tetrahedron cross configuration, transforming chemistry into a predictable, continuous spectrum of macroscopic matter-vibration frequencies.