Gravitational Curvature as Structured Entropy: Three-System Validation of the QIR DeltaX Equation

We present observational validation of the Quantum Information Gravity (QIR) framework across three gravitational systems: a galaxy cluster (Abell 1689), a collisional cluster (the Bullet Cluster), and a spiral galaxy (NGC 3198). The QIR equation ∆X, rooted in a curvature-memory formalism, reproduces gravitational lensing and rotational velocity patterns without invoking dark matter. Each prediction uses only luminous mass, spatial geometry, and a derived entropy field. Each system’s gravi-tational behavior is matched using visible mass and entropy alone, without requiring dark matter.