Completing the DBQTM: Inflation from a Third Warped Throat

We complete the Dual-Brane Quantum Tunneling Model (DBQTM) by introducing a third Klebanov--Strassler throat as the inflationary sector. In the companion papers~{DBQTM-Paper1,DBQTM-Paper2}, two warped throats on the same Calabi--Yau manifold were shown to generate the cosmological constant (Throat~1: K₁=203, M₁=17, kd₁ ≈ 375) and dark matter (Throat~2: K₂=39, M₂=35, kd₂ ≈ 35, mDM ≈ 133~GeV). A shallow third throat with (K₃, M₃) = (3, 27) and kd₃ ≈ 3.5 provides a GUT-scale IR sector at ΛIR,3 ≈ 6.5 × 10¹⁵~GeV. The K\"ahler modulus of this throat, stabilized via the KKLT mechanism with $SU(27)$ gaugino condensation, naturally produces a Starobinsky-like α-attractor inflationary potential (α = 1), predicting nₛ = 0.964 and $r = 0.004$, both consistent with Planck and testable by LiteBIRD and CMB-S4. The scalaron decay produces a reheating temperature TRH ≈ 2.5 × 10⁹~GeV, precisely in the range required for gravitational freeze-in production of the dark matter candidate in Throat~2. All three cosmological sectors --- dark energy, dark matter, and inflation --- are thus determined by seven discrete flux integers (K₁, M₁, K₂, M₂, K₃, M₃, gₛ) and one continuous parameter (k/MPl), with verifiable cross-predictions linking the inflationary observables to the dark matter abundance.