Golden-Angle Prime Spirals and Random Models II: Pair-Kernel Mechanism and Robust α Diagnostics

Part I established a cross-window-stable coarse-bin signature for the golden-ratio family under a squared angular-contrast diagnostic on prime spirals. Here we formalize the pair-kernel mechanism responsible for the multi-B response and define an explicit anti-alias protocol for meaningful α comparisons on discrete bin panels. Using the gap-to-angle map ∆θg = 2παg (mod 2π), we interpret coarse-bin structure with the standard same-bin overlap kernel based on circular distance, Kstd(∆θ; B) = max(1 − δ(∆θ)/w, 0). We define geometry-only weights Wgeom g (B) ∝ Kstd(∆θg; B) and geometry×pair-count weights Weff g (B) ∝ Wgeom g (B)Mg for even gaps g ≤ Gmax = 300, and evaluate predictions on the segmented panel B ∈ {20, 30, 40, 44, 48, 60, 80, 100, 120} across two disjoint prime windows. For the golden-ratio family (α = φ −2 and α = φ −1 ), the standard pipeline reproduces the observed multi-B response with strong, window-stable correlation and preserves the dominant B = 60 top-set structure reported in Part I. Kernel-envelope substitutions and an explicit α–B commensurability screen indicate that the leading structure is not an artifact of panel arithmetic. Series note. This paper is Part II of a three-part series and provides the mechanism and robustness specification for the shared coarse-bin instrument. The consolidated unified presentation appears in “A Coarse-Bin Angular-Contrast Instrument for Prime Spiral Resonances and Quantum Channel Eigenphases,” TechRxiv (2025), doi:10.36227/techrxiv.176585133.32280606/v1.