CHRONOTAXIS AND SEMICLASSICAL QUANTUM GRAVITY: Induced Newton Constant and Cosmological Constant Screening via Branch Entropy Suppression

This manuscript extends the Chronotaxis phi-branching geometric framework into the domain of semiclassical quantum gravity. By treating the five-dimensional branch field as a quantum fluctuation upon a classical spacetime background, we derive a complete, falsifiable framework that addresses the core anomalies of modern cosmology and black hole physics. Key Results: Induced Gravity: Utilizing Seeley-DeWitt heat-kernel proper-time methods, we integrate out branch field fluctuations to induce the Einstein-Hilbert action. We derive the Newton constant (Gind) directly from branch microphysics without fine-tuning. Cosmological Constant Screening: We demonstrate that the O(10¹¹³ J/m^3) vacuum energy divergence is naturally suppressed by the de Sitter horizon entropy (SdS), yielding an effective dark energy density that matches observation to within ~40%. Singularity Resolution: Using a 1D polar-areal Misner-Sharp numerical relativity framework, we establish analytic and computational thresholds where localized branch stress-energy halts gravitational collapse. Chronology Protection: We provide a mathematical theorem proving that branch superselection rigorously forbids the formation of closed timelike curves (CTCs). Emergent Quantum Geometry: An extension to the Wheeler-DeWitt equation demonstrates how classical WKB time emerges directly from branch decoherence. The manuscript concludes with six quantitative, falsifiable experimental predictions, including specific phi-harmonic targets for Quantum Random Number Generators (QRNGs), CMB multipole analysis, and gravitational wave dispersion.