This paper presents a definitive deterministic framework that goes far beyond the probabilistic constraints of Riemann’s Hypothesis, offering more than just an analytical proof. By decoupling the continuous rotational boundary of complex zeros and removing the geometric factor π, we reveal the "Purified BaBa Pattern" where Riemann zeros transform directly into an exact, step-by-step prime-counting mechanism. Using the dynamic sieve coefficient λ (x) = x/n, we eliminate long-standing statistical fluctuations and bridge the gap between classical analytical geometry and the absolute certainty of primorial matrix sieves. Furthermore, we resolve the transfinite divergence dilemma, proving that λ (x) is structurally bound and converges monotonically to a localized rigid barrier of exactly 2. 00 at infinity, shielding the system from chaotic fluctuations or unexpected reversals. This version (V2) expands the empirical calibration up to the submillennial astronomical scales of 10²2 using Odlyzko's datasets, establishing a strict log-linear structural smoothness and absolute boundary containment. Keywords: Riemann Hypothesis, Purified Riemann Zeros, Prime-Counting Function, BaBa Pattern, Dynamic Sieve Coefficient, Asymptotic Convergence, Deterministic Sieve Geometry.
Albaba,, Mohammed K. A. (Sat,) studied this question.