Quantum Mirror Hypothesis: Velocity-Dependent Self-Interacting Dark Matter from a Mirror Scalar Field

This is a speculative effective field theory preprint. We propose a complex mirror scalar field ϕ with soft U(1) breaking (ε ≈ 0.012) that naturally generates a velocity-dependent SIDM cross-section. The primary falsifiable prediction is a Yukawa-mediated momentum-transfer cross-section σ_T/m_ψ ∼ 1–10 cm²/g at dwarf velocities (v ∼ 10–30 km/s), falling to ≲ 0.1 cm²/g at cluster velocities (v ∼ 1000 km/s), consistent with current astrophysical data. A distinctive QMH signature is a ∼1.2% mass splitting between the real and imaginary mediator modes. Baryogenesis connections are included only as qualitative Sakharov-consistent pathways requiring future numerical work. This preprint supersedes earlier versions and focuses on a clean, quantitative SIDM prediction with honest assessment of limitations. Full PDF attached.