Geometric Bridge via Gravitational Standing Waves: A Midscale ΔD Framework Connecting α and Λ

This manuscript presents a midscale geometric mechanism that bridges the local fine-structure constant $\alpha$ and the global cosmological constant $\Lambda$ within the three-tier hierarchy of Bulk Network Cosmology (BNC). The core mechanism involves gravitational standing waves formed at the bulk boundary, whose nodal structures generate three stable phases that geometrically fix the three fermionic generations. These intermediate phases define a midscale dimensional mismatch $\Delta D_{\text{mid}}$ that mediates between the local dimensional mismatch $\Delta D_{\text{local}}$ and the global dimensional mismatch $\Delta D_{\text{global}}$ through an equiproportional scaling coefficient $r \approx 1.43$. The paper provides a theoretical formulation, numerical verification, and observational predictions (such as GW echoes and $\alpha$ time variation), demonstrating that $\alpha$ and $\Lambda$ may derive from a common geometric origin.