Topological Solution to the Strong CP Problem from Pin+ Bordism Four-Layer Constraint Framework and θQCD = 0

【[Strong CP Problem Series-Paper 4】Strong CP papers 1-4 are sufficient to solve most of the problems in strong CP. We propose a topological solution to the strong CP problem from the 4-dimensional Pin⁺ bordism group Ω₄Pin⁺ = Z₁₆. The solution operates through a four-layer constraint framework: (Layer 1) Pin⁺ invariance requires θ_QCD = 0 in all topological sectors; (Layer 2) the Z₁₆ bordism structure classifies 16 distinct topological sectors; (Layer 3) in each sector k, the effective angle θ_eff = θ_F(k) = πk/8 arises as a chiral field ground state topological shift in the infrared layer, not as a path integral θ shift in the ultraviolet layer; (Layer 4) sector k = 0 is dynamically selected by vacuum energy minimization, cascade tunneling, and the neutron EDM constraint. This UV-IR separation resolves the apparent paradox that the bordism phase e^(iπk/8) is a global (configuration-independent) phase in the path integral yet produces sector-dependent physics: the physical effects manifest entirely through the chiral field ground state Σ₀(k) = e^(−iθ_F(k)τ₃/Nf) in the low-energy effective theory. We respond to the Kaplan-Melia-Rajendran argument [15] that parity cannot solve the strong CP problem by distinguishing Pin⁺ as a cross-superselection-sector topological constraint from intra-sector parity symmetry, and noting that Kuchimanchi [16] independently proves θ ∈ {0, π} from Hilbert space structure, providing a double independent proof. Domain wall tension σ(0, k) = 8f_π²m_π sin²(πk/64) provides dynamical distinction with hierarchical stability, and all Z₁₆ domain walls decay within 10⁻⁶ s after the QCD phase transition—far before big bang nucleosynthesis. Three decisive experiments distinguish our solution from the Peccei-Quinn mechanism: axion detection, CMB TB/EB polarization, and gravitational wave spectroscopy.