Hierarchical Black Hole Mergers

Quantised Spacetime Framework SigmaP (QSTF) and Hierarchical Black-Hole Mergers This work presents a parameter-free synthesis between Quantum Mechanics and General Relativity, built upon an invariant Planck two-measure SigmaP=lptp=hbarG/c^4 By interpreting spacetime as composed of finite, quantised cells of this measure, curvature, action, and vacuum energy become naturally self-consistent.The framework resolves the “vacuum catastrophe” by re-scaling, rather than renormalising, the relationship between quantum-field and cosmological vacuum densities, leading to 1.ΛQFT/Λobs=1. When applied to black-hole mergers, this discretised geometry predicts that coalescences proceed through hierarchical, multi-phase interactions rather than continuous fusion.Each merger reorganises local spacetime cells in discrete steps, emitting gravitational waves at each stage — a geometric necessity that directly aligns with recent observations of repeated, high-spin black-hole collisions (LIGO/Virgo/KAGRA, 2024–2025). The Quantised Spacetime Framework (QSTF) thus provides a unified, scale-invariant foundation connecting microscopic quantisation with macroscopic curvature.No new constants, parameters, or dimensions are introduced; the solution was always contained within the known physical constants — we merely had to assemble them correctly.