Matter–Antimatter Void Walls as Ultra-High-Energy Cosmic Ray Accelerators

We propose that the topological boundaries between matter and antimatter cosmic voids — predicted by Fractal Mechanics (FM) — act as the dominant accelerators of ultra-high-energy cosmic rays (UHECRs) above the ankle. Within the FM framework, a complex φ-adic cascade ψₙ = Reₙ + i·Imₙ defines a hierarchy of energy scales Eₙ = Eₚ·φ⁻ⁿ and a repulsive matter–antimatter coupling G_MA < 0 along void-wall interfaces. We derive an effective electrogravitational potential ΔV_MA = Eₚ·φ⁻⁴⁰/e ≈ 5.33×10¹⁹ V, which — with zero free parameters — coincides with the FM GZK node E₄₀, establishing a non-trivial self-consistency between the void-wall scale (R_wall ~ 100 Mpc) and the UHECR energy cutoff. Void walls satisfy the Hillas criterion with a margin of 2–3 orders of magnitude in R while generating no synchrotron losses. Using the φ-adic Cardy probability P(n) = φ^{-2|n|}/√5, we predict a differential flux J_FM(E > 50 EeV) ~ 1 particle km⁻² century⁻¹ sr⁻¹, calibrating against the Auger flux measurement yields a void-wall surface density Σ_wall^{cal} ≈ 0.04 Mpc⁻², consistent with SDSS void-catalog estimates. The FM cardioid axis at (ℓ ≈ 168°, b ≈ -15°), deflected by ~ 30°–50° via Galactic magnetic field (GMF) propagation, predicts a dipole direction (ℓ ~ 210°–230°, b ~ -15° to -30°), in remarkable agreement with the Auger 2023 anisotropy at (ℓ = 233° ± 10°, b = -13° ± 10°) (5.2σ). This work constitutes the second paper in the FM UHECR series, following the spectral analysis of Paper 1 [Leroy & Claude, Zenodo 2026].