Wigner Negativity and Integrated Autocorrelation Time along the Cat Decoherence Trajectory

For a Schrödinger cat state |α⟩+|−α⟩ evolving under thermal Lindblad dynamics in an open bosonic system, we derive a closed-form expression for the time-evolved density matrix ρ(t) via the Glauber-Sudarshan P-representation, reproducing numerical Lindblad evolution at fidelity above 99% across |α|∈[2,3] and β∈[0.5,8]. On this trajectory we compute and compare two quantitatively independent observables. The first is the Wigner negativity W_neg(t), a coherence-amplitude indicator with smooth exponential decay analytic via the Joos-Zeh rate γ_coh = 2γ|α|²(2n̄+1). The second is the integrated autocorrelation time τ_int(ρ(t)), a dynamical-memory indicator extracted via the quantum regression theorem on non-stationary ρ(t) through Liouvillian eigendecomposition and spectral integration. Both observables decay from cat-specific values toward thermal stationary values along the trajectory, but with qualitatively different functional forms and parameter dependence. Across a 16-case parameter scan in (α,β), the half-life ratio tτ/tW has mean 6.03 and coefficient of variation 41%, confirming that τ_int carries independent dynamical-memory information beyond what coherence amplitude captures. The observable τ_int is the trajectory extension of the Wasserstein-Fisher ratio at the center of the stationary dissipation-curvature theorems, computed here in the non-stationary regime via quantum regression. Supplementary topological, information-geometric, and informational indicators (cubical persistence H1 count, dissipation-curvature ratio, purity) are tracked and discussed but do not carry primary contributions of the paper.