Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Regularizing Strong-Field Gravitational Wave Source Environments and Metric Fluctuations for Project LISA

This special treatise delivers the formal mathematical physics formulation and non-linear metric stabilization tracks designed exclusively to regularize strong-field gravitational wave backgrounds and sub-Hz frequency tensor fluctuations required for Project LISA (Laser Interferometer Space Antenna) instrumentation profiles. Operating within the exact analytical framework of Trans-Planckian Horizon Lock Mechanics (TPHLM), we demonstrate that highly non-linear cosmic perturbations generated by compact binary coalescences and extreme mass-ratio inspirals do not collapse into divergent singularities near the mathematical horizon boundaries.