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 — a geometric characterisation of the Yang–Mills mass gap. Paper 5 in the Planck Lattice series. Previous papers: neural oscillations (DOI: 10.5281/zenodo.19267675), cross-domain survey (DOI: 10.5281/zenodo.19312741), driver analysis (DOI: 10.5281/zenodo.19312939), deuteron identity (DOI: 10.5281/zenodo.19323770). Dataset (WS_ATLAS_EXPANDED.csv), scatter plot, and the open-source Planck Lattice Mapper tool are included. Version 5.2. Developed with computational assistance from Claude (Anthropic). All scientific claims and intellectual contributions are the author's.