This monograph presents the "Leakage Hypothesis" extension for the Dual Brane Cosmogenesis (DBC) framework. Using MCMC simulations (emcee) against the Dark Energy Survey (DES) Year 6 dataset, we establish preliminary constraints on the leakage coupling parameter ($\alpha_0$). Our findings suggest a physical mechanism where black holes function as trans-dimensional valves, allowing energy/information to tunnel into a coupled Dark Brane while retaining baryonic residue on the visible brane. This asymmetric transfer prevents mathematical singularities and provides a repulsive "information pressure" that triggers a non-singular Big Bounce. APA (7th Edition) Bryant, N. (2026). Five-dimensional wave propagation and the tertiary brane dynamics in Dual Brane Cosmogenesis [Research monograph]. Zenodo. https://doi.org/[Insert-DOI-Here] MLA (9th Edition) Bryant, Nicole. Five-Dimensional Wave Propagation and the Tertiary Brane Dynamics in Dual Brane Cosmogenesis. Research Monograph, Zenodo, 27 Apr. 2026, https://doi.org/[Insert-DOI-Here]. Chicago Manual of Style (17th Edition) Bryant, Nicole. 2026. "Five-Dimensional Wave Propagation and the Tertiary Brane Dynamics in Dual Brane Cosmogenesis." Research Monograph. Zenodo. https://doi.org/[Insert-DOI-Here]. Harvard Style Bryant, N., 2026. Five-Dimensional Wave Propagation and the Tertiary Brane Dynamics in Dual Brane Cosmogenesis. Research Monograph. Zenodo. Available at: https://doi.org/[Insert-DOI-Here].