Eternal Universe Theory – Mirror Edition E(u₁) = –E(u₂) Axion-Fused Two-Sheeted Energy-Antisymmetric Cosmology Integrating Temperature-Dependent Ultralight Scalar Dynamics

The Mirror Edition v0.3 fuses a two-sheeted spacetime U₁ ⊕ U₂ with exact antisymmetry E(u₁,x) = –E(u₂,x) and a temperature-dependent ultralight axion-like particle (ALP) from EUT v5.2. The ALP mediates inter-sheet tunneling via primordial Planck-scale PBH pairs as ER=EPR bridges, yielding self-regulated dark energy Λ_eff = 8πG ⟨J_E⟩ of observed magnitude. An early stiff phase (w = +1, ∼64 e-folds) ameliorates horizon/flatness problems without inflation. Late-time solitonic cores (1.1–1.8 kpc) match dwarf galaxy observations, with mild sextic self-interaction λ₆ ≈ 10⁻⁹⁴ ensuring superradiance compatibility (Nov 2025). The model is eternal, singularity-free, information-preserving, zero total energy, and predicts testable w(z) deviations and void friction effects for Euclid/DESI/LSST. Added: Appendix E : Zeta-Mirror Symmetry / Riemann Hypothese Added Appendix F Quantum Bridges in Mirror Cosmology – Resolving P=NP and Hodge Conjecture Appendices G & H: Mirror Cosmology Extensions – Quantum Fields, Fluids, and Elliptic Ranks