This paper presents an algebraic framework that integrates recursive expansive dynamics, fractal geometry, and non-Archimedean corrections through the introduction of constructs such as the Inverse Zero Operator (IZO) and Influence Operators. This theory models complex physical systems where interactions are influenced by prior states and semi-SUSY-recursive feedback mechanisms. The framework addresses spacetime propagation, energy dissipation, and information storage mechanisms in higher-dimensional structures. Theoretical foundations are established through geometric templates like trochoids epicycloids, hypocycloids, and Hyper Limacon caustics. Constructed through fixed-point theorems, metric deformations, holographic entropy scaling. Hyperaddition and Hypermultiplication are defined with correction functions that incorporate fractal scaling and p-adic effects. We then build a layered model that smoothly transitions from quantum-scale operations (using Jordan algebras) to macroscopic feedback (modeled via loops and near-rings). Finally, we integrate these ideas with adelic Gromov-Witten theory and p-adic quantum geometry.