The Hurwitz Fibre Decomposition at Zeta Zeros

We decompose the Hurwitz zeta function ζ(s, a/60) at non trivial zeros of ζ(s) according to the Hopf fibre structure of S³/2I. The 60 residue classes mod 60 = |A₅| are grouped by edge (mod 4), face (mod 6), and vertex (mod 10) fibres. Trivial slots— those divisible by the fibre's construction prime — vanish identically because their Hurwitz sums factor as c(s) × ζ(s). Non-trivial slots cancel in exact antisymmetric pairs with ratio −1 for edge and face fibres, driven by their unique non-trivialDirichlet characters. For the vertex fibre, three characters contribute, including the Legendre symbol (n/5) whose Gausssum is exactly √5 = φ − ψ, identifying L(s, (·/5)) as the L function of the golden number field ℚ(√5). A key correction(from v2.0): the edge/face antisymmetric pairing R = −1 is algebraically forced at any zero of ζ, not specific to the criticalline — the Hurwitz multiplication formula makes these cancellations trivial consequences of ζ(s) = 0 regardless ofRe(s). The vertex fibre, with its three characters including the order-4 golden pair χ₂, χ₃, is the only fibre with sufficientstructure to carry a critical-line constraint. This redirects the search for an RH criterion from the edge/face architecture tothe vertex's golden content.