Lawrence Cyclic Interdependency Principle (LCIP) Complementary Cyclic Structure of Prime and Non-Prime Digits in π

This research introduces the Lawrence Cyclic Interdependency Principle (LCIP), specifically focusing on base 10, where harmonic resonance and cyclic interdependency of prime and non-prime digits are uniquely observed. Through Fourier Transform analysis, Binary Density Factor (BD) calculations, and fractal dimension metrics, the study uncovers structured harmonic patterns that challenge the assumption of π’s randomness. Unlike other bases, base 10 exhibits pronounced harmonic stability, revealing a non-random and structured digit distribution. These findings open new avenues for research in number theory, harmonic analysis, and cryptographic applications. Code: https://github.com/JaniqueLW/harmonic-resonance-pi