The proof to the RH may involve the knowledge of real analysis, general topology, ( f : x+yI =Rζ:Cx,y,Iζ:Cx,y∈RXR → Z = dRζx+yI,Iζx+yI∈R
where d = |f (x’, s’)| = |(Rζx'±Iy-RζRs'±Iy,Iζx'±Iy-IζIs'±Iy)| (f may be extended from a 4th dimension R4 (or CXC) to the R) or the norm and is defined byRζx+yI2+Iζx+yI2with x,y∈R from a complex number’s order pair (most likely to be the values of the non-trivial zeta zeros) to a real number or the vice versa with some suitable statistical optimization method to adjust, separate x’ and y’ from Z and find the values in the vice versa original complex ordered pair (x’, y’) or x’ + y’I through the inverse mapping f -1 :Z = dRζ-1±εx+Rζx'-Rs'±Iy,±εy+Iy-Iy∈R→x’+y’I = Rζ:Cx',y',Iζ:Cx',y'∈RXRwhich is actually the set of the non-trivial zeta zeros etc.) In other words, the above is obviously a complex plane geometry with a projection onto the real numbered line, mathematic-a programming & algebraic modulus theories. One may first need to define those real analysis theories in terms of metric space or general topology. Then we have to draw and shift those lines and curves in a complex plane printed by the mathematic-a software such that we may observe those natural and human made artificial optimal non-trivial zeta zeros on the real and complex axis. Finally, we may apply the algebraic modulus theories to show that x = 0.5 is the one and only one optimal non-trivial zeta zeros while others are just the angular rotational of it. We may further used the aforementioned result(s) for the encryption-decryption which is an interesting topic for any further research.
The following is the outline steps:
1.The function that links the point from 0.1 to 0.9 with the fixed imaginary complex component part for every given non-trivial zeta root(s) (one at a time) must always be a continuous function (but not all of the continuous functions must lie between the interval 0.1 and 0.9), otherwise any discontinuous implies commercial engineering impulse;
2. Changing sign from negative to positive (by the immediate value theorem) there must be an optimal root between [0.1, 0.7]. As we have shown that, f (0.5) = 0, f (0.5) must be the optimal point, i.e. the optimization;
3.Angular rotation of the other intersection points = intersection point at x = 0.5;
4.0.5 is the unique optimal point;
5.RH is true (or false if you consider the other infinite many angular rotation intersection points as the different form of roots to the Riemann Zeta function by a shift of a delta high) where x =0.5 is the only optimal root and others are not the optimal roots. This ends the forward part of the Riemann Hypothesis. The RH will be true or false depends on whether one may recognize those artificially human made non-trivial zeta zeros. (N.B. The mirror imaged “inverse Riemann Hypothesis” problem may usually refer to the spectral problem and the operator one. I employ the mirror imaged “inverse optimization” as a replacement. In such a case, the spectral and operator method may thus involve an inverse operator (transformation or mapping) as an alternative proof to the Riemann Hypothesis for a verification (or a control). I will leave to those interested parties for an in-depth study as a comparison with my present proof so that we may have a fine calibration in the topic of the Riemann Hypothesis research. Actually, my present study is a private one and I do not have so much resource(s) to work for everything (either employ a professional programmer or a computer typing secretary and other research related persons etc).
To conclude, x = 0.5 is the most optimized point (saddle) among all of the equilibrium points in the critical region for 0 < x < 1. Or, all of the other equilibrium points between 0 < x <1, are actually NOT the best optimized one at x = 0.5.
