The Primorial Sparse Zeta Root (Delta = Po1) and Golden-Angle Quasi-Periodicity: A Damped Fibonacci Construction

We establish a number-theoretic construction linking the primorial sparse zeta root Δ = Po1 ≈ 1.13783917..., defined by S(Δ) = 6/π² where S(α) = ∑ Pn-α and Pn is the n-th primorial, to golden-angle quasi-periodicity through a damped Fibonacci recurrence. The damped sequence defines coefficients ck = rk ei k θ with r = 1/Δ ≈ 0.8788588264. The associated multiplication operator on ℓ²(₀) belongs to every Schatten class Sp (p > 0) with explicit norms. The variational functional Jθ admits a closed-form expression whose critical-point structure is analyzed analytically. Comparative numerics and sensitivity analysis demonstrate local robustness near the golden angle θg = 2π/φ² relative to generic damping factors. High-precision asymptotics, entropy compression rates, and falsifiable predictions are provided. Potential objections to the bridge are addressed in the appendices. Research Context: This manuscript functions as an operational, exploratory toy model extension of the foundational framework established in "A Primorial Sparse Zeta Function with Root S(α) = 1/ζ(2)". It maps the analytical convergence boundaries of the established Po1 root directly to quasi-periodic structural distributions.