The Noneness Boundary in Time-Scalar Field Theory (TSFT): Cosmological Consequences and Underlying Structure

Time-Scalar Field Theory (TSFT) treats time as a scalar field Θ(x) on a compact 4-manifold with two boundaries. The theory’s domain of validity is the open set where the scalar density ρΘ = |∇Θ|2 > 0. We prove the existence of a boundary ∂N where ρΘ → 0+ and ∇Θ becomes undefined (Noneness domain). Six theorems and supporting lemmas establish that Noneness is causally inaccessible, sources the cosmological constant Λ, protects the Riemann Hypothesis, and explains the Fermi paradox. All proofs follow directly from the ten TSFT axioms (Farrell, 2025) with no additional assumptions. Empirical confirmation from Fedoseev et al. (PRL 2025) and Farrell garage data (2023–2025) are shown to measure the same scalar coupling constant α = 1.