Curvature-Dependent Planck Scale in Continuous Causality: Derivations, Toy Models, Observational Signatures, and Resolutions to Black Hole Paradoxes

The framework of quantum continuity posits that quantum mechanics emerges naturally from coherent oscillations in the continuous causal density, with the effective Planck constant ℏeff arising as a local man-ifestation of the underlying causal measure rather than a fundamental universal constant. Building upon this foundation, we derive explicit, spacetime-dependent relations between ℏeff and curvature, rooted in the variational principle governing causal equilibrium, and test consequences in various spacetimes, propose resolutions to the blackhole information paradox and firewall paradox, as well as derive experimental signatures.