Finite-Area Stolz Images at Almost Every Plessner Point

We extend Oleg Ivrii’s Gaussian lacunary construction by slowing its variance clock. If deterministic positive variances satisfy v_n <= C/n, sum v_n = infinity, and sum v_n/log(n+1) < infinity, then almost surely the holomorphic series sum sqrt(v_n) xi_n z^(2^n) has almost every boundary point Plessner, while every Stolz image there has finite planar Lebesgue measure and the areas of truncated images tend to zero. Area is taken without multiplicity. The hypotheses hold for v_n = 1/[n(log(n+1))^beta] for every fixed 0 < beta <= 1. The proof adapts Ivrii’s dyadic shadowing and Brownian embedding, adding a summable covering by unit-time Wiener sausages. Ivrii’s September 2026 preprint already answered the Collingwood and Baernstein questions (Hayman-Lingham 5.20 and 5.57) negatively; this note is a finite-area strengthening, not a first solution of those questions. The five-page English manuscript contains the complete proof. AI-assisted and self-audited; no independent peer review, formal verification, or exhaustive priority certification is claimed.