Resolution of the Cosmic TeV Gamma-Ray Transparency Paradox via Vacuum Elastodynamics: Kinematic Threshold Shifts and High-Frequency Shear Hardening in a Pre-Stressed Substrate

Ground-based Imaging Atmospheric Cherenkov Telescopes (H.E.S.S., MAGIC, VERITAS) and space-borne observatories have established the persistent detection of very-high- energy (VHE, E ≥ 1− 20 TeV) gamma rays from distant blazars at cosmological red- shifts (z ≥ 0.1− 0.3). In standard relativistic quantum electrodynamics, intergalactic space should be effectively opaque to these photons due to electron-positron pair creation on the Extragalactic Background Light (EBL) via the Breit-Wheeler process (γVHE +γEBL → e+ +e−), predicting an exponential spectral cutoff that is absent or signif- icantly suppressed in empirical data. Rather than postulating exotic hypothetical par- ticles such as axion-like particles (ALPs) or ungrounded Lorentz-symmetry violations, we resolve this “TeV transparency paradox” directly from the continuum elastodynam- ics of the physical vacuum. We demonstrate that electromagnetic waves are trans- verse shear stress impulses propagating within an elastically pre-stressed medium en- dowed with an elementary unit cell ℓ0 ∼ 10−35 m and characteristic impedance Z0. At extreme TeV frequencies, the wavelength of the excitation approaches the nonlin- ear response regime of the continuum, producing a dynamic shear-hardening of the substrate impedance Z(ω) and shifting the kinematic Breit-Wheeler threshold toward higher center-of-mass energies. This natural suppression of pair-production cross- sections renders the intergalactic medium transparent to TeV photons while preserving linear Lorentz invariance across all lower-energy observational bands.