Restricted Greedy Prime Decomposition, the Meissel-Mertens Constant, and a Structural Proof of the Riemann Hypothesis

This document formalizes the connection between a combinatorial greedy prime decomposition algorithm (restricted to residues different from 1), the Meissel-Mertens constant (M), and the Riemann Hypothesis (RH). We prove that the cumulative sums of the diagonals of the decomposition matrix exhibit strictly quadratic growth with coefficient A = 2M. By modeling this growth using a generating zeta function and applying Perron’s convolution formula, we prove that the structural error term is spectrally bounded by the geometric rigidity of the diagonal sieve. This strict combinatorial bound forces the non-trivial zeros of the Riemann zeta function to lie exclusively on the critical line ℜ(s) = 1/2.