Emergent Causal Spacetime and Einstein Gravity from Wedge Modular Inclusions

We present a mathematically closed, self-consistent framework for the joint emergence of local causal spacetime, gauge symmetries, quantum fields, and Einstein gravity from a single ontological primitive: a half-sided modular inclusion of a hyperfinite type III1 Von Neumann algebra. Using Borchers’ and Wiesbrock’s theorems, we show that local Poincaré covariance and a Haag-Kastler net of local algebras emerge naturally, resolving the lo- cal causality gap. Connes’ Radon-Nikodym cocycle theorem provides a state-independent canonical outer modular flow, solving the time problem. We prove that the Einstein-Hilbert action is a stable infrared attractor of the spectral RG flow, suppressing higher-derivative ghost-like terms in the macroscopic limit. We formulate a complete quantum scattering theory via the Haag-Ruelle framework, establish the physical rigidity of the Standard Model as a unique Morita equivalence class, and present a hard, non-deformable Popperian fal- sifiability boundary based on Starobinsky inflationary parameters