A Geometric Origin for the Cosmological Constant from CPT-Symmetric Branes: Framework, Flux Stabilization, and Topological Quantization of 𝜌 Λ

Abstract We present the Dual-Brane Quantum Tunneling Model (DBQTM), a geometrically motivated framework for the cosmological constant based on a CPT-symmetric two-brane configuration in a Randall--Sundrum (RS) background with Goldberger--Wise (GW) stabilization. The observed vacuum energy arises from the inter-brane mixing suppression $\rho_\Lambda = k^4 \cdot \exp(-n_\mathrm{geo} \cdot kd)$, with $k = 0.0869\,M_\mathrm{Pl}$, $n_\mathrm{geo} = 0.720$, and $kd \approx 375$.The 122-order-of-magnitude hierarchy between the natural and observed vacuum energy scales is recast as a moderately large geometric product $n \cdot kd \approx 270$. We derive the Binetruy--Deffayet--Langlois junction conditions self-consistently, showing that the physical brane tension $\lambda_\mathrm{eff} = V_A/2 \approx 0.09\,M_\mathrm{Pl}^4$ exceeds $\rho_\mathrm{crit}$ by $10^{120}$, making $w(z) = -1 + \mathcal{O}(10^{-119})$. A no-go theorem establishes that vacuum energy suppression and observable BDL corrections are mutually exclusive within the RS framework. To address the question of \emph{why} $kd \approx 375$, we explore four flux-stabilization mechanisms. The most natural is a Klebanov--Strassler embedding, where the brane separation is determined directly by quantized 3-form fluxes: $kd = 2\pi K/(g_s M)$. With $g_s = 1/5$, $K = 203$, $M = 17$, we obtain $kd = 375.14$ and $\rho_\Lambda$ within 2\% of the observed value. The cosmological constant becomes a topological invariant --- a consequence of two integers characterizing the flux threading the compactification manifold. \medskip\noindent\textit{v2.0}: Adds parameter scans (Appendix~A),flux vacuum stability via CDL/HM instantons (Appendix~B), andcritical comparison with six competing frameworks includingranked limitations (Section~5). Core physics unchanged.