Convergence Width on the Planck Lattice: A Dimensionless Binding Measure Across Four Fundamental Forces

We define the spatial convergence width W_s = |a_mass − a_size| on the Planck Lattice logarithmic coordinate system, computed from independently measured mass and spatial extent. Across 57 physical systems spanning four fundamental forces, W_s anti-correlates with binding fraction (Spearman ρ = −0.890, p = 2.0 × 10⁻²⁰, n = 57; ρ = −0.847, p = 3.2 × 10⁻¹⁴ with gravitational systems excluded). QCD hadrons cluster at W_s ≈ 0.1–0.7, nuclei at 1.3–3.8, electromagnetically bound systems at 5.4–12, and gravitational objects span 0.7–10.5. For gravitational systems, W_s = −log₁₀(GM/Rc²) reduces to an algebraic identity with the compactness parameter. Planck Lattice addresses 1–16 constitute a convergence width desert…