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The proof converts omission into four zero-free entire functions $Q_j$ attached to the stem function. For affinely independent target points, the coordinate normal to their affine span is governed by a square-discriminant identity $T^2=\\Delta_A(Q_0,Q_1,Q_2,Q_3)$. 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We prove that a nonconstant entire slice regular function on $\\mathbb H$ can omit these four values if and only if they are affinely dependent. Thus the affinely independent case, the four-point borderline left open by the Bisi--Winkelmann Picard theorem, cannot occur. The proof converts omission into four zero-free entire functions $Q_j$ attached to the stem function. For affinely independent target points, the coordinate normal to their affine span is governed by a square-discriminant identity $T^2=\\Delta_A(Q_0,Q_1,Q_2,Q_3)$. 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