Algebraic Scalars, Logarithmic Lifts, and the Exact Escape Boundary

With L_alg = exp⁻¹(Q̄^×): for 0 ≠ λ ∈ L_alg, βλ ∈ L_alg iff β ∈ Q (Gelfond–Schneider), and B·λ ∈ L_alg^s iff B is rational (Baker); branch shifts are rational scalings; and individual transcendence does not give joint algebraic independence.