The pitch-angle anisotropy and the inversion to wave-growth time. Panel (a): the first-order anisotropy A_1,N versus proton energy, with rigidity on the top axis. Colored filled markers show the observed A_1,N from EPI-Lo in three upstream windows and one downstream (see legend). Open markers show the near-shock upstream and downstream anisotropies after the Compton–Getting correction to the plasma frame. The solid blue curve is the upstream DSA ceiling ﹩{A}_{1}^{{\rm{DSA}}}=3{u}_{1}/v﹩, and the dashed purple line at A_1,N = 0 is the downstream steady-state DSA reference (isotropy in the plasma frame). The gray region (﹩{A}_{1}^{{\rm{DSA}}}\gt 1﹩) marks where the small-anisotropy diffusion approximation breaks down (see Appendix C). The purple-shaded band marks the confinement–escape transition E_x ≈ 2–5 MeV, bracketing the downstream A_1,N sign reversal in the spacecraft frame. Panel (b): the temporal evolution of the observed spectral folding energy E_fold (red circles). The inner error bars show the statistical uncertainty, and outer bars show the statistical and systematic uncertainties combined. The solid blue curve is the power-law fit E_fold ∝ Δt ^α, and the shaded band is the 68% confidence interval from the bootstrap method described in the text. Panel (c): the inferred wave-growth timescale τ_growth versus folding energy. Red circles show the panel (b) data reexpressed as (E_fold,i,  Δt_i) pairs. The solid blue curve is the uniform-Γ_k inversion τ_growth(E) ∝ E^1/α, and the shaded band is its 68% confidence interval. The dashed orange line marks the precursor convective timescale τ_EP, and the star marks the E_c where the two timescales meet.