Contextual Semantic Collapse: A Theoretical Simulation of Non-Commutative Behavior of Geometric Frameworks for Valuation in the Built Environment

Abstract

Standard valuation methodologies, specifically Discounted Cash Flow (DCF), rely on the additivity axiom, assuming that "Financial" and "Social" capitals are commutative, independent variables that can be linearly aggregated. This paper challenges this "Additivity Assumption" when using a Geometric-Semantic Valuation Model (GSVM) (e.g., Transformer-based Large Language Model). Drawing on the mathematical formalism of Quantum Cognition, we model the built asset not as a static object, but as a normalized state vector |ψ⟩ within a high-dimensional semantic Hilbert space. We demonstrate that the Financial and Social valuation frameworks are non-commuting projection operators (p fin , p soc ] ≠ 0). Through a simulation of N=100 distinct asset descriptions, we provide a computational demonstration of path dependence: the order of valuation perspectives (projectors) alters the asset's final overall value (from an ontological-state perspective). Where the initial projection onto a "Finance" subspace yields a significantly more constrained ontological state than the "Social" first strategy, which preserves greater aggregate dimensionality and overall system value.