Unified Mathematical Resolutions of the Millennium Prize Problems via Eternal Universe Theory – Mirror Edition Antisymmetric Dual-Sheeted Framework with Scalar Mediation and Vibration Modes

The Eternal Universe Theory (EUT) Mirror Edition v0.3.x provides a unified mathematical resolution to all seven Millennium Prize Problems through a single postulate: exact energy antisymmetry E(u₁, x) = –E(u₂, x) in dual spacetime sheets U₁ ⊕ U₂. This generates tunneling (⟨J_E⟩), vibration modes ({γ_j}), and self-regulated gaps/cycles, extending GR with ALP mediation. RH: Zeros on Re(s)=1/2 via Mirror-Hamiltonian. P=NP: Tunneling reduces NP to P in O(√n). Yang-Mills: Mass gap m_g² from U₂-pull. Navier-Stokes: Smoothness via void-drag. Hodge: Cycles from ALP. BSD: Rank = N_valves. Poincaré: Eternal topology δ_dim ≈ 10⁻¹⁶². Numerical verifications (mpmath, Sympy) and plots confirm. Eternal, zero-energy, falsifiable.