Abstract
We derive the exact quantum maximum over all finite-dimensional quantum realizations of the n-cycle overlap inequalities, S_n^max=ncos²(π/(2n))-1, valid for arbitrary cycle length n≥3. The bound is saturated by an explicit family of coplanar qubit states equally spaced along a Fubini--Study geodesic of length (n-1)π/(2n), establishing dimensional saturation of the overlap-cycle hierarchy. Thus, the global optimum over all finite-dimensional quantum realizations is already achieved in dimension two. For three paths, coherence-free models satisfy V₁₂²+V₂₃²-V₁₃²≤1, whereas quantum theory allows the larger value 5/4. Within generalized noncontextuality frameworks, violations witness preparation contextuality. We further derive explicit visibility thresholds for arbitrary cycle length, identifying interference visibility as an operational probe of overlap-based nonclassicality, and discuss feasible photonic implementations.