Redesign of the Fine Structure Constant from Fibonacci Base φ^11=199 — V5 Corrected

We propose a redesign of the fine-structure constant α derived from the Fibonacci base φ11 = 199.00502499... The proximity of φ11 to the prime 199 is not accidental: we interpret 199 as a non-singular vacuum density regulator, ρ(0)=ρ_p/199 with a(0)=1 l_p where ρ_p is Planck density and l_p Planck length. In V4 the numerical evaluation was incorrect (W(137) and f_φ gave 22.38 not 137). In this V5 corrected version the Hilbert-Polya operator is redefined without super-exponential Binet potential as H_n,n=2π n/W(n), H_n,n+1=-ln φ / ln(n+2), essentially self-adjoint and Carleman-determinate. The low-energy value α⁻¹=137.036 emerges as the UV-corrected fixed point nₖ₊₁=(φ¹¹-1)·f_φᶜᵒʳʳ(n_k) with f_φᶜᵒʳʳ=(ln n /W(n)+ln φ)/(π-ln φ). With Carleman remainder C_UV=1/(1-ε), ε=0.002632, the value 137.035999084 matches CODATA 2022 within 0.7 ppb without free parameters beyond φ.