Adelic Fractal Cosmogenesis Recursive Number-Theoretic Scaffolding of Spacetime Geometry and Cosmic Observables

This paper presents a fundamental reorientation of numerical cognition through Base-0 mathematics, establishing primes as oscillatory resonance nodes in negation-stabilized void-space. We develop a recursive stabilization framework using the Plastic Number (ρ ≈ 1.3247) and Silver Ratio (δs ≈ 2.414), revealing fractal patterning in prime gaps that challenges classical number-theoretic assumptions. The Zeta Zeno Zero function Z(x) = P∞ n=1(−1)nn −x emerges as a critical operator encoding negation oscillations, with applications in quantum cryptography and AI architectures. Our axiomatic system bridges holographic void encoding with quantum vacuum fluctuations through retrocausal negation dynamics. This work further extends to recursive scaffolding of number-theoretic geometry and observational cosmology, demonstrating that exotic material behaviors are manifestations of spacetime’s intrinsic fractal-recursive geometry.