Applied ITT — Executable Physics III: Topological Discourse Analysis

Applied ITT — Executable Physics III: Topological Discourse Analysis Armstrong Knight (Sensei Intent Tensor) · intent-tensor-theory.com We prove that the ZETA index ζ = sign(κ) × round(r/Δ) approximates the Euler characteristic of the phase interface of the Allen-Cahn semantic field. The Euler characteristic is a topological invariant: it can only change through discrete topological transitions corresponding to qualitative changes in discourse mode. We classify discourse trajectories by their ZETA dynamics and connect the framework to RST, SDRT, and the Gauss-Bonnet theorem. Key results: Theorem 4.1: ζ ≈ (4−χ(S))/2. Theorem 4.2 (Homotopy Invariance): ζ preserved under homotopic deformations. Four discourse trajectory classes (Convergent, Resonant, Divergent, Lock). Conjecture 4.1: ζ ≈ cyclomatic complexity + 1 of SDRT discourse graph. Part of the Applied ITT — Executable Physics series. Builds on WP-02. Continues in WP-04. Repository: https://gitlab.com/intent-tensor-theory.com-group/git-0-0-applied-intent-tensor-theoryWebsite: https://intent-tensor-theory.com