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We derive the transverse-traceless (TT) gravitational wave sector of Density Field Dynamics (DFD) from the same CP²×S³ internal manifold that produces the fine-structure constant, fermion mass hierarchy, and MOND interpolation function. The scalar field ψ (governing quasi-static gravity) and the tensor h_ij^TT (governing gravitational radiation) are shown to be the trace and TT components of a single parent strain tensor, which is itself the zero mode of the metric perturbation on the internal manifold. A Lichnerowicz analysis on CP²×S³ proves that no unwanted massless tensor or vector modes arise from internal deformations (CP² gap = 8/R₁², S³ gap = 12/R₂², b₁ = 0). One scalar modulus (the squashing mode controlling R₁/R₂) survives; we prove it is uniquely determined at the Einstein product condition τ* = 1/√3 by the joint α-G constraints from the spectral action, acquiring a Planck-scale mass (Φ''/Φ = 2.94, no parametric suppression). The gravitational sector contains exactly 1 scalar + 2 tensor degrees of freedom. The generalized Tamm-Plebanski construction gives anisotropic constitutive relations with compression stiffness K₀ = c⁴/(8πG) and shear stiffness K₀/4, with the E/B split parameter κ = α/4 derived from gauge emergence. Source coupling reproduces the quadrupole formula identically to GR. Sector decoupling is proven from O(3) irreducibility; c_T = c exactly. The two-sector structure of the DFD Unified Review is thereby promoted from introduced to derived from the same topology that produces α⁻¹ = 137.036. The Einstein product condition creates a new cross-link in the DFD architecture: the same self-consistency condition that fixes G·ℏ·H₀²/c⁵ = α⁵⁷ also determines the internal geometry, guaranteeing the correct graviton mode count. Companion paper to the DFD Unified Review v3.3 (DOI: 10.5281/zenodo.18066593).