The Fibonacci Spectral Ladder: Hopf Fibre Decomposition of the Zeta Spectrum on S³/2I

The Poincaré homology sphere S³/2I admits a Seifert fibration with three singular fibre types: vertex fibres (wrapping 5 times, stabiliser Z₅), face fibres (wrapping 3 times, stabiliser Z₃), and edge fibres (wrapping 2 times, stabiliser Z₂). We decompose the spectral multiplicity function of S³/2I into explicit contributions from each fibre type and show that the vertex contribution — the golden component — follows a period-10 cycle whose values are {2/5, 0, 1/5, 0, 0, 0, −1/5, 0, −2/5, 0}. The character recursion generating this cycle has coefficient 2cos(2π/5) = 1/φ, which is the Fibonacci recursion. Consequently, the eigenvalue thresholds at which irreducible representations of 2I first appear in the branching from SU(2) are organised by a triple-rail ladder: the Fibonacci sequence (chiral), the Lucas sequence (achiral), and a single face-closure rung at D! = 6 = |S₃|. Together, these three rails account for all nine representation thresholds. The spectral gap λ₁ = 168 = 13² − 1 = F₇² − 1 is the seventh Fibonacci rung. We verify numerically that the first zeros of Dirichlet L-functions sort into spectral bands defined by these thresholds, with each prime conductor mapping to a specific representation band of 2I.