The energetic-particle precursor and the compressive amplitude over 06:00–07:13 UT on 2023 March 13; the time axis corresponds to shock-normal distance through x = u₁(t_shock − t), and the dashed line marks the shock. (a) Energetic-particle pressure P_EP (green) with its exponential fit of scale length L_EP ≃ 5.48 R_⊙ (black dashed). (b) The compressive amplitudes δn/n (maroon) and δB_∥/B₀ (black), the in-phase coherent components in the LP-OB band (Appendix C), with the energetic-particle-gradient forced response ﹩{ \mathcal N }/({M}_{f}^{2}-1)﹩ (gray dotted).