This paper presents the Causal Virtual Machine (CVM), the execution engine responsible for transforming CSL (Causal Specification Language) programs into evolving causal geometries running directly on the Causal Kernel. Unlike traditional virtual machines that interpret instructions, manage stacks, simulate hardware, or coordinate threads, the CVM operates in a purely geometric paradigm. Its computational units are π-nodes, √2-relations, √3-curvature surfaces, φ-flows, and ln 5-dissipation fields — the five fundamental CT constants. The CVM parses CSL code into a Causal Abstract Syntax Graph, constructs the corresponding causal manifold, and evolves it through φ-propagation and ln 5 dissipation until convergence to a stable geometry. Execution is continuous and causal rather than stepwise. The system enforces the four Patriarch Theorems — contraction, orthogonal decomposition, curvature–growth inequality, and entropy–dissipation — ensuring that every configuration remains valid and internally coherent. This work provides the full architecture of the CVM, including parsing rules, graph construction, flow dynamics, dissipation mechanics, invariant enforcement, safety guarantees, and example executions. It establishes the CVM as the central bridge between the Causal Kernel (CT hardware) and CSL (CT language), defining a new class of computation where programs stabilize as geometric attractors rather than instruction sequences. From the same author: causality theory CT united https://zenodo.org/records/17366521 10.5281/zenodo.17366521 causality united v2 https://zenodo.org/records/17564091 10.5281/zenodo.17564091