Applied ITT — Executable Physics II: Semantic Field Equations

Applied ITT — Executable Physics II: Semantic Field Equations Armstrong Knight (Sensei Intent Tensor) · intent-tensor-theory.com We derive a complete semantic field equation system from three coupled dynamics: graph Laplacian diffusion (semantic smoothness), Allen-Cahn phase separation (shell formation), and intent anchor projection (gauge constraint). The system has a unique fixed point — proved via Banach fixed-point theorem — whose equilibrium state encodes semantic coherence as minimum-energy phase separation in the Ginzburg-Landau free energy functional. Shell formation is proved to be minimum-energy phase separation, not an imposed categorization. Key results: Theorem 3.1 (Phase Separation): Allen-Cahn gradient flow converges to thin-interface configuration. Theorem 3.2 (Existence and Uniqueness): unique fixed point φ* ∈ 0,1ⁿ by Banach fixed-point theorem. Parameter stability condition proved. Five-equation system fully derived. Part of the Applied ITT — Executable Physics series. Builds on WP-01. Continues in WP-03. Repository: https://gitlab.com/intent-tensor-theory.com-group/git-0-0-applied-intent-tensor-theoryWebsite: https://intent-tensor-theory.com