Riemann hypothesis errors’ estimation & its commercial a.i. control system suggestion

Error estimation for the E(x) = ψx-x has been a long time discussion hot topic for most of the mathematicians research. In the present paper, this author tries to relate some the significant number theorem(s) and equation(s) between the Riemann Zeta function and the Prime Distributions together with my previous results in the magnified proof in the Riemann Hypothesis – x = 0.5 is the only saddle point among all of the equilibrium points in the critical region 0 < x < 0.9 (in fact these equilibrium points and the only saddle point) are the intersections between Rζx+yI=Iζx+yI,) where Rζx+yI is continuous and x = 0.5 is unique as well as there is only one pole at x = 1 (this author will prove them in details). At the same time, all of the other points excluding x = 0.5 will oscillate to spread for both sides with the equilibrium point laying in the middle. Certainly, there is also a mirror image converse for the above depicted Riemann Hypothesis picture which will be listed in a table format at the end of this author’s conclusion section. Moreover, from the sandwiched logarithmic equations between the Prime Number Theorem’s error estimation, we may further employ the Fourier & its Inverse Transform together with the Laplace Transform and its Inverse Transform so as to get the modified Zeta function without the pole “1”. By mapping the “1” to ez through the Z-transform we may further get the wanted “Zeta Filter” and in the mirror inverse Z-transform, we may also find the “Prime Filter”. All of these filter may be in practice useful in applying to solve our present cryptography for the encryption and decryption etc. Last but not least, this author will end the present research project with an operator model plus the conclusion paper in cryptography.