The Riemann Zeros as Golden Interference: Four Movements Toward a Proof from S³/2I

We present a geometric framework for the Riemann Hypothesis based on the spectral geometry of the Poincaré homology sphere S³/2I. The argument proceeds in four movements. First, the non-trivial zeros of ζ(s) exist because periodic analytic tools are applied to an intrinsically aperiodic structure — the golden wavefront on S³/2I, whose aperiodicity is guaranteed by Klein's theorem that A₅ is non-solvable. Second, the zeros are confined to Re(s) = ½ by two mechanisms: a symmetry (the functional equation is golden conjugation φ ↔ ψ, whose fixed axis is Re(s) = Re(φ) = ½) and a rigidity (the spectral gap λ₁ = 168 of S³/2I, which kills eleven eigenspaces and forbids the soft modes needed for off-axis corrections). At Re(s) = ½, every Dirichlet term has magnitude n^{−½} = √(n^{−φ}·n^{−ψ}), the geometric mean of golden growth and golden decay. Third, GUE statistics are explained in a companion paper as a consequence of the spectral gap silencing low-frequency modes. Fourth, the Fibonacci spectral ladder — Fibonacci, Lucas, and face-closure thresholds covering all nine representation thresholds of 2I — sorts L-functions by conductor into spectral bands. We reframe the Hilbert-Pólya conjecture: the operator should be golden-Hermitian (self-adjoint under √5 ↔ −√5) on S³/2I, yielding rational eigenvalues rather than merely real ones. The 110-year search for the operator was conducted in the wrong algebra (ℂ instead of ℚ(√5)) on the wrong space (ℝ instead of S³/2I).