π Tadpole Tail Fluctuation Theory

As a core mathematical constant, π has long been considered to have an infinite, non-repeating, and random decimal sequence. Through ultra-high-precision numerical calculations and interdisciplinary theoretical derivation, this paper discovers an inherent fluctuation law based on prime-order truncation in the decimal places of π — the π Tadpole Tail Fluctuation. This law is not only an inherent mathematical property of π but also the core underlying operating law of the universe. Integrating fourth-order discrete derivatives and high-order cumulative integrals, this paper constructs a logically consistent and numerically reliable interdisciplinary theoretical framework. With the unified characteristic quantity Ψₙ as the core, it completes the derivation of core constants and laws in multiple disciplines without empirical parameters, relying only on the inherent value of π and prime number sequences. The results are highly consistent with existing experimental values, providing a new path for basic scientific research.