Resolution of the GZK Paradox via Substrate Acoustic Phase Detuning: Non-Linear Photopion Suppression and Extended Propagation Horizons for Trans-GZK Cosmic Rays in an Elastically Pre-Stressed Vacuum

In standard relativistic astrophysics, ultra-high-energy cosmic rays (UHECRs) are bounded by the Greisen-Zatsepin-Kuzmin (GZK) limit (E_GZK ≈ 50 EeV), above which resonant photopion production on the CMB (p + γ_CMB -> Δ -> N + π) restricts their propagation horizon to D_GZK ≤ 50–100 Mpc. However, multi-decade observations by the Pierre Auger Observatory, the Telescope Array, and historical arrays have recorded multiple trans-GZK events exceeding 100 EeV—including the 320 EeV "Oh-My-God" particle and the recent 244 EeV "Amaterasu" event—arriving from cosmic voids devoid of nearby accelerators. Standard models invoke decaying superheavy dark matter (ruled out by photon limits) or ad-hoc Lorentz Invariance Violation. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that trans-GZK propagation is an intrinsic consequence of acoustic phase detuning in the substrate. In our ontology, a proton is a topological strain soliton, and photopion creation is the resonant excitation of its internal breathing mode. For ultra-relativistic Lorentz boosts (γ ≳ 10^11), the dynamic shear stress localized within the contracted soliton envelope exceeds the background pre-stress P_0, inducing an acoustic phase-slip that detunes the resonant overlap with the CMB shear field. We analytically derive the suppressed cross-section σ_eff(s) = σ_BW(s) [1 + (s - s_th)/s_0]^-2, showing that the cosmic attenuation length expands from 50 Mpc to >1200 Mpc for energies E ≥ 100 EeV. This explains the arrival of trans-GZK cosmic rays from distant cosmological blazars under Occam's razor without speculative decaying relics or broken relativity.