We show that the (+) -involution on the Katz 2-adic L-function of a CM motive forces a double zero at T = 0, and that the leading coefficient is a 𝔓-adic unit. The vanishing c₁ = 0 is of a different nature from both exceptional zeros in the sense of Mazur–Tate–Teitelbaum and trivial zeros arising from Γ-factors; it is intrinsic to the signed projection. The sharpening to ordₓ=₀ Lₚ^+ (T) = 2 with c₂ ∈ ℤₚ× follows from the p-adic Colmez formula, since the balanced CM type forces the Katz period ratio to be a 𝔓-adic unit. We then convert this analytic double zero into arithmetic congruences on Hecke units of unbounded depth: for ray class families ℛₑ of positive Chebotarev density, every q ∈ ℛₑ satisfies v_𝔓 (u (𝔮) − 1) ≥ 2e. The genus barrier for the Fermat octic is completely classified, with σ̃q (8) = 0 only for q ∈ 17, 41, 113. final edited version
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