9D-USTE Continuation: 4D Foliated Hypersurface, Kinematic Propagation of 3-D Spatial Leaves and the Origin of Emergent Time

In previous work within the Nine‑Dimensional Universal Unified Evolution Theory of Entropic Topology (9D‑USTE), multiple papers have investigated topological phase transitions, black‑hole‑Big‑Bang duality, scalar‑field dynamics, dark‑matter and dark‑energy topological interactions, and the topological origin of the arrow of time. Those publications adopted a 4‑dimensional spacetime framework, where the evolution parameter t was presupposed as a fundamental coordinate; they successfully unified thermodynamic, cosmological, causal and quantum time‑arrows via winding‑number dilution and the universal topological invariant, yet they did not address the physical ontological origin of time itself. In this paper we upgrade the framework: the 4D foliated hypersurface embedded in the 9D closed simply‑connected mother manifold contains no fundamental time coordinate. Our observable three‑dimensional universe corresponds to instantaneous 3‑dimensional spatial leaves of this 4D hypersurface labelled by the hidden‑dimension coordinate w. Observable time emerges from continuous propagation of these 3D spatial leaves along the hidden spatial coordinate w. The winding‑number‑dilution topological dynamics inherited from former 9D‑USTE theory acts along the hidden dimension w, providing the driving force for leaf propagation together with topological protection that forbids time‑reversal evolution. The extra gravitational effect conventionally attributed to dark matter originates from residual‑curvature differences between the full 4D geometry and the truncated 3D‑leaf geometry. We adopt a generalized ADM‑like 3+1 decomposition for covariant description of the leaf family, analyse compatibility with local Lorentz invariance, derive analytical expressions for curvature residual, and provide magnitude estimates for falsifiable observational signals. The present work constitutes a sequential iterative extension, rather than a refutation, of the earlier 9D‑USTE series. All topological invariants, winding‑number rules, black‑hole physics, scalar‑field results and cosmological predictions from prior publications are fully inherited and reinterpreted via chain‑rule mapping onto the hidden‑dimension parameter w. Two logically consistent global ontological realizations (single hypersurface versus topologically‑branched multi‑hypersurface scenario) remain open questions for future investigation, whereas the core conclusion of emergent observable time holds for both realizations.