M18c The Halbzeug: Spectral Theory and the Riemann Hypothesis

This monograph develops the spectral theory of the Halbzeug and formulates a precise Halbzeug‑based Riemann programme. The critical line Re(s)=1/2 is identified as the Halbzeug of the s‑plane: the unique self‑dual locus under the ±Balance involution s ↦ 1−s. The Halbzeug is thus the arithmetic midpoint between identity and absorber domains. M18c constructs the NC spectral staircase, inserting half‑levels between integer cascade absorbers, and shows that this staircase is the natural skeleton of the zero distribution. Halb‑primes and the associated Halb‑zeta function are introduced, together with the Skew Principle and the Skew‑zeta tower. The monograph connects Halbzeug dynamics to Fatou/Julia penetration of the NC quadratic at the critical parameter and develops cycle polynomials and Atow₃ spectral theory. The Riemann Hypothesis is reformulated as gap symmetry: any zero off the critical line would violate the proven Halbzeug symmetry.