A Spherical N-Series Area Law for Regular Refinement Families

This paper presents numerical evidence for an even-power area-error law in regular, scale-consistent spherical refinement families. Across four regular refinement families, the observed asymptotic convergence sequence follows the pattern 2→4→6→82 \\to 4 \\to 6 \\to 8 under successive Richardson–Romberg scale cancellation. The study also examines perturbed refinement families to identify the boundary at which the regular even-power structure degrades. Exact conditional scale-cancellation and moment identities are established, while the general spherical even-power area law itself is presented as a conjectural structural principle supported by the numerical experiments. The accompanying repository contains the manuscript, numerical scripts, reproducibility documentation, and generated verification outputs.