Metalogical Foundation of the Spatial Architecture and Ambient Universe (SAA)

Abstract

This document outlines the metalogical foundations of the Spatial Architecture and Ambient Universe (SAA). By operating within an Intuitionistic Topos and adhering to Constructive Mathematics, the SAA formally rejects the Law of Excluded Middle and the Axiom of Choice. This paper defines the spatial universe as a coproduct of a discrete Skeleton ($Z$) and a continuous Pointless Locale ($U$), establishing the core axioms required to insulate the system from classical set-theoretic paradoxes.