Axion-Photon Coupling in the E8-X Unified Field Theory

We compute the axion–photon coupling constant \( gaγγ \) from first principles within the \( E_8 \)–\( X \) Unified Field Theory. The axion emerges naturally as a pseudo-Goldstone mode from the spontaneous symmetry breaking \( E_8 → E_6 × SU(3)_F \), corresponding to a topological pseudo-scalar component of the fundamental field \( X ∈ 248 \). Using the unique representation theory of compact \( E_8 \) and the anomaly cancellation structure, we derive a parameter-free prediction \[gaγγ ≈ 1.24 × 10⁻¹⁷ \, GeV⁻¹,\] which lies within the sensitivity reach of current and next-generation axion experiments. This result provides a sharp, falsifiable signature of the \( E_8 \)–\( X \) theory. ---