Adaptive Constraint Cascade (ACC): Part Test – A Testable Prediction (Quantum–Classical Lineshape Crossover in a Driven Qubit)

We derive a testable prediction from the Adaptive Constraint Cascade (ACC) framework, specifically from ACC_1 (quantum–classical transition). Using the ACC_1 framework equation – a Lindblad master equation with a λ-dependent dissipation rate γ(λ) = γ₀ tanh(λ), where λ = k_B T / ħω₀ – we compute the emission spectrum S(ω) of a qubit (two-level system) as a function of temperature T. The theory predicts a continuous crossover from a narrow Lorentzian peak (coherent regime) at low T to a broad Lorentzian peak (incoherent regime) at high T, with the linewidth Γ following Γ(λ) = Γ₀ + β tanh(λ), where β is a constant determined by the system–bath coupling. Rather than introducing a fundamentally new dynamical law, ACC provides a unified structural interpretation of crossover behavior that is often modeled using separate approximations in different regimes. Experimental verification is feasible with current superconducting qubit or trapped-ion platforms. We outline a concrete experimental protocol.