Infogravity 4.3+ : Mathematical Foundations of Informational Spacetime Geometry

Infogravity 4.3+ establishes a fully mathematical foundation for the Infogravity programme, in which spacetime geometry, gravity, and temporal ordering emerge from the information geometry of coarse–grained quantum states. Building on the structural principles of Infogravity 4.2 and the dynamical constructions of Infogravity 4.3, this work formalises projection as a fundamental operation and proves that informational monotonicity uniquely selects the Fisher information metric as the admissible geometric structure. Spacetime is shown to arise as the pull–back of this metric, while gravitational curvature is identified with residual informational curvature surviving coarse–graining. The framework further demonstrates the co–emergence of entropy and time, establishes no–go results excluding stable non–geometric representations, and introduces effective stratification as an organisational principle for interaction regimes. Infogravity 4.3+ thus shifts the programme from interpretive motivation to structural inevitability, positioning emergent spacetime geometry as a necessary consequence of informational consistency rather than a postulated background.