Entropy-Inflection Collapse in Five Dimensions

This work presents a five dimensional framework for quantum collapse that defines reduction as happening on entropy inflection surfaces where the flow of information flattens.

The model is built on a corrected scalar operator that properly accounts for the radial volume measure and the spectrum of compact topologies.

By applying a variational principle with a Lagrange multiplier, the theory produces dual field constraints, a conserved stress energy sector for collapse, a non negative entropy current, and a defocusing condition that replaces singularities with a finite Planck scale shell.

We carry out the separation of variables and reduce the system to a Schrödinger form with an explicit potential, leading to clean predictions for observables such as photon sphere location, shadow size, and echo delays, while also tracking how topology and extra dimensional mass terms shift quasinormal modes and sidebands.

The model includes consistent boundary conditions at the horizon or shell, a corrected Tolman Oppenheimer Volkoff interior with proper geometric weights, a post Newtonian limit that recovers general relativity, and a numerically stable scheme for evolving wavepackets.

In the matter sector the approach derives hydrodynamic equations, a quantum kinetic functional with dimensional consistency, and a finite volume discretization that reduces to the Many Interacting Worlds model in one dimension.

The framework is directly testable in the lab through attosecond scale collapse timing and EEG entropy plateaus, and in cosmology through coherence signatures and microwave background anomalies.