On the Projection Structure P* and its Realization by the Riemann Xi-Function

This work presents the definitive theorem edition (v1.0) of the Projection Structure P* formalism. Building on the specification series v0.1–v0.4, we rigorously prove that all zeros of the Riemann xi-function lie on the critical line Re(s)=1/2 and are simple. The proof combines: (i) a seven-axiom abstract framework with digit symmetry and ontological separation between real arithmetic space R and computational complex space C; (ii) group-action fixed-point analysis showing Fix(G)={1/2}; (iii) Hardy space H^2 norm obstruction barring any zero off the critical line; (iv) contour phase mismatch for symmetric zero pairs; and (v) monodromy obstruction for multiple zeros. The Riemann Hypothesis is thereby established as a structural necessity of the P* symmetry constraints, not merely a conjectural statement. Complementary to noncommutative geometric approaches (Connes), this work derives the critical line from first principles of projection symmetry.