The Perfect-Square Law for Distinct-Variable 2-Color Rado Numbers of x + by = bz

We prove that R(x + by = bz, 2; distinct) = b^2 for all integers b >= 4, where R is the 2-color Rado number with distinct-variable convention. The lower bound follows from the canonical 'multiples of b red, non-multiples blue' coloring. The upper bound combines a Structure Lemma (in any 2-coloring of {1, ..., b^2-1}, all multiples of b in this range share a single color) with a Two-Triple Blocking argument. The Structure Lemma is proved by an Alternating Cascade for generic (b, k) pairs together with explicit case analyses for the three exceptional pairs (b, k) in {(4,1), (4,2), (5,1)}. The proof is fully analytical with no SAT-only steps; SAT verification for b = 4..50 is provided as a cross-check. This resolves Conjecture 2 from the companion Rado-families paper (Towell, 2026, Zenodo DOI 10.5281/zenodo.19212447). v2 (April 27, 2026): Revised version following internal review.