Non-Equilibrium Many-Body Universality, Active Matter, and Multiscale Turbulence Physics (NEMBAMT): A Deductive Framework Unifying Dissipation–Information Bounds, Certified Multiscale Closure, and Inverse Metamaterial Design within the ZFC Axiomatic Bridge

Equilibrium statistical mechanics relies on free-energy minimization (δF = 0), which fundamentally fails for strongly correlated non-equilibrium quantum matter, self-propelled active matter, multiscale plasma and fluid turbulence, and inverse-designed metamaterials. In this paper, we establish the Non-Equilibrium Many-Body, Active Matter, and Multiscale Turbulence (NEMBAMT) framework, unifying and upgrading items #9 (Quantum Many-Body Universality and Non-Equilibrium), #12 (Universal Laws of Active Matter and Non-Equilibrium Complex Systems), #13 (Multiscale Integrated Physics of Turbulence and Plasma), and #15 (Physics of Designable Matter and Effective Laws) of the 20 Emergent Physics Agenda. Anchored in our 71-page ZFC Master Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) and synthesized with the SVKES coarse-graining abstraction and HDGPS statistical-dimension phase transition frameworks, we formulate multiscale non-equilibrium dynamics across the Fractional Sobolev–Colombeau Quotient Hierarchy 𝒢^α(Ω) = ℰ_M^α(Ω) / 𝒩^α(Ω) governed by 𝔘 = (𝒯_0x8A2C, C_UPTC, η_friction, ε_SHID). We establish six core axioms (NEMBAMT-1 through NEMBAMT-6) and prove six fundamental theorems: (1) Universal Dissipation–Information–Order Variational Principle Ω_NE(Ψ_m) = Ṡ_prod(Ψ_m) − κ_eff I_trans(𝒳_ℓ ; Ψ_m) + η_friction ‖Ψ_m‖² replacing equilibrium free energy, together with the UPTC-sharpened Thermodynamic Uncertainty Relation Var(J_curr) / ⟨J_curr⟩² ≥ 2 / (Ṡ_prod + κ_eff I_trans − η_friction); (2) UPTC Quotient Invariant Emergence where coarse-graining projections Abstractℓ→m: 𝒳_ℓ → 𝒳_m with information loss ΔI_loss ≥ H_shan(𝒳_ℓ) − C_UPTC > 0 absorb microscopic details of fiber size |F_y| ≥ 2^(ΔI_loss) into the Colombeau null ideal 𝒩^α(Ω), proving that macroscopic universality classes depend solely on the quotient symmetry group Aut(F_y) and Sedenion topological gap ℒ_𝒯(M̂) ≥ c_𝒯 > 0; (3) Certified Multiscale Turbulence and Plasma Closure with global smoothness ‖∇Ψ_m(t)‖_L∞ ≤ C_UPTC / ε_SHID < ∞ via the Harmonic Brake ℬ_ε and uniform L² closure error bound O((ℓ/m)^α_Col · κ_eff⁻¹) + η_friction; (4) Dual Predictability Theorem separating finite pointwise Lyapunov horizon T_traj = λ_max⁻¹ ln(Δ_tol / δ₀) from infinite-horizon Sinai–Ruelle–Bowen (SRB) ergodic measure concentration 2 exp(−κ_eff T ε² / 2); (5) Statistical-Dimension Phase Transition Theorem for Inverse Metamaterial Design, proving that dynamically stable, fabricable microstructures θ* ∈ 𝒟_meta with manufacturing tolerance radius r_fab ≥ ε_SHID / √C_UPTC exist with probability ≥ 1 − 2 exp(−u²/8) whenever design degrees of freedom satisfy m_design ≥ δ(𝒟_meta) + u√(C_UPTC / κ_eff) with δ(𝒟_meta) = C_UPTC; and (6) Universal Non-Equilibrium Transport Scaling Plateau D_trans / Ṡ_prod → (c_𝒯 ε_SHID C_UPTC)⁻¹ at strong drive. Complete Python numerical verification is provided in Appendix A.