Sci - Delta Dynamics: The Pre-Geometric Control Theory of Threshold States

Sci - Delta Dynamics: The Pre-Geometric Control Theory of Threshold States Armstrong Knight — intent-tensor-theory.com — 2026 The Dimensionless Mathematics framework (T4-16 through T4-21) establishes the conditions under which stable structure exists. What it does not provide is a dynamical theory of the threshold itself — not merely what must be true for structure to exist, but what governs the threshold as a movable object, how it evolves, and what physics looks like when the full pre-geometric Delta control vector is projected down through each dimensional layer. This paper introduces Delta Dynamics as the control theory of threshold states in the ITT framework, organized around two complementary perspectives. The bottom-up perspective describes emergence: how dimensional structure accumulates as the scalar pre-geometric substrate acquires gradient bias (0D→1D), recursive memory (1D→2D), and closed boundary persistence (2D→3D). The top-down perspective describes restriction: how the full six-component pre-geometric Delta control vector Δ⃗ = (Δ₁...Δ₆) loses degrees of freedom at each dimensional layer, identifying what physics becomes inaccessible at each projection as an instance of the Dimensional Plane Error applied to Delta itself. The paper derives the complete Delta control law — gate score G_Δ = σ(S_sel−1)·∏σ(k_net−θ_k), control potential V_Δ = −ln G_Δ + η(Δ₃−Δ₄)², and equation of motion λ̇_Δ = −Γ∇_λV_Δ — validates them across Yang-Mills gauge theory, nuclear stability (SEMF bridge), Schwarzschild black holes (Page turnover at t* ≈ 0.339·t_evap without importing island formula), and Kerr rotating black holes (spin-delay ∂t*/∂a* > 0 confirmed). The Universal Coordinate Ledger (UCL v1.0) is frozen as the operational baseline. The nested reality equation ρ_obs = β_cos · β_loc(W) · ρ_substrate connects local objecthood to the cosmic containment ratio. Six open derivation problems are precisely stated.