A Formal Resolution of Spacetime Singularities via Information Sealing: Quantum Formalism and Observational Signatures of BQGF

This paper presents BQGF v11, a framework that resolves black hole singularities through saturated non-minimal coupling F(ψ) = 1 + ξ tanh(ψ²/M_p²) and a Topological Locking mechanism enforced via Lagrange multipliers. The theory achieves global geodesic completeness by replacing the classical singularity with a regular Planck Core, where curvature invariants remain finite. A hierarchical self-consistent solution is constructed: asymptotic General Relativity in the exterior region, topological soliton phase in the core, and smooth Israel junction matching. The framework is ghost-free (verified via Dirac-Bergmann analysis), preserves unitarity through topological information sealing, and predicts a deterministic 7.9 ms gravitational wave echo delay for 10 solar mass black holes, accompanied by a characteristic Sinc² vacuum noise signature. These predictions are falsifiable with next-generation detectors such as the Einstein Telescope (ET) and LISA. This work represents a paradigm shift from phenomenological metric patching to a fundamental interaction regularization approach in quantum gravity.