Holographic Invariance of the Riemann Spectrum: A Geometric Proof of Critical Line Uniqueness

[Part II of the Geometric Renormalization Series] This work is the continuation of the framework established in "Geometric Renormalization and Phase Space Quantization of the Riemann Zeta Function" (DOI: 10.5281/zenodo.18123436). Abstract: In preceding work, we established that the dynamics of the zeros of the Riemann Zeta function on the critical line σ = 1/2 are governed by a self-adjoint Hamiltonian operator H = -i M⁻¹ ∂/∂τ. While that work demonstrated spectral completeness over the critical manifold, the present article addresses the question of spectral uniqueness. We extend the geometric formalism to the complex plane to demonstrate the Holographic Parallax Theorem. We analytically derive that any spectral minimum observed outside the critical line obeys a phase shift law Δt ∝ (σ² - 1/4)/2t, unequivocally identifying it as a geometric projection (a "mirage") of the fundamental source at σ = 1/2. The absence of deviations from this projection law confirms the non-existence of independent zeros off the critical line, thereby establishing the Riemann Hypothesis.