WATSON EXPANSION AND BOREL STRUCTURE FOR CLASS A; ASYMPTOTICS OF CLASS B IN NON-HOLOMORPHIC FRACTAL FAMILIES

We derive the complete Watson expansion for the Class A stable-area law A(K) ~ C_A K^{-γ_A} arising in non-holomorphic fractal families of Bird's classification. The expansion is a two-saddle decomposition: the interior saddle at t → 0 produces a convergent hypergeometric series G^A(w) = _2F_1(1/2, p; p + 3/2; w) in integer powers of w = K^{-(1+α)/2}, whose Borel transform is entire; the endpoint boundary layer at t → 1 contributes a second convergent series in the incommensurable power w^{3/(1+α)^2}, generically irrational and invisible to any finite truncation of the Watson series. The leading boundary-layer coefficient is C_bl = (2/3)√(2(1+α)) R^{3/2}, proved in closed form. A complete set of Watson…