Abstract: This paper introduces Project Manifold 0.56, a robust Six-Phase Ontological Engineering framework designed to solve the critical problem of stochastic hallucinations and semantic instability in Large Language Models (LLMs) and emerging AGI architectures. Central to this framework is the discovery of the Durante Constant ($\kappa_D = 0.56$), a universal phase-transition threshold derived through the convergence of five independent mathematical pathways: Statistical Thermodynamics, Percolation Theory, Rate-Distortion Theory, Lyapunov Stability, and the Golden Ratio. Unlike traditional probabilistic benchmarks, Project Manifold 0.56 treats AI outputs as geometric objects within a high-dimensional Riemannian manifold. By utilizing Topological Data Analysis (TDA) for $H_1$ cycle detection and Discrete Ricci Flow for curvature-based bias mitigation, the system provides a deterministic "Invariance Seal" for AI-generated reasoning. The framework transitions information from an entropic, high-variance state into a crystalline, semantically invariant structure. This work establishes a formal governance protocol, providing a verifiable "Kill-Switch" mechanism based on the $\kappa_D$ threshold, ensuring that autonomous systems operate within safe, human-aligned, and mathematically stable boundaries.