The 1859 Riemann hypothesis conjectured all nontrivial zeros in Riemann zeta function are uniquely located on sigma = 1/2 critical line. Derived from Dirichlet eta function [proxy for Riemann zeta function] are, in chronological order, simplified Dirichlet eta function and Dirichlet Sigma-Power Law. Computed Zeroes from the former uniquely occur at sigma = 1/2 resulting in total summation of fractional exponent (-sigma) that is twice present in this function to be integer -1. Computed Pseudo-zeroes from the later uniquely occur at sigma = 1/2 resulting in total summation of fractional exponent (1 - sigma) that is twice present in this law to be integer 1. All nontrivial zeros are, respectively, obtained directly and indirectly as the one specific type of Zeroes and Pseudo-zeroes only when sigma = 1/2. Thus, it is proved (using equation-type proof) that Riemann hypothesis is true whereby this function and law rigidly comply with Principle of Maximum Density for Integer Number Solutions. The geometrical-mathematical [unified] approach used in our proof is equivalent to the algebra-geometry [unified] approach of geometric Langlands program that was formalized by Professor Peter Scholze and Professor Laurent Fargues. A succinct treatise on proofs for Polignac's and Twin prime conjectures (using algorithm-type proofs) is also outlined in this anniversary research paper.