A Lorentzian Sector Bundle over the Geometric-Time Direction Sphere

This upload contains a self-contained kinematic paper developing the Lorentzian sector-bundle layer of the multi-geometric-time Omniverse formulation. The paper studies an ambient vector space with three ordinary spatial directions and a positive K = ξ − 3 dimensional geometric-time block. Its central distinction is between the scalar clock parameter t, the ordinary Minkowski time coordinate x⁰ = ct, the ambient geometric-time coordinates, the selected geometric-time carrier Ĝ, and the effective geometric-time coordinate G₀. A selected unit geometric-time direction Ĝ ∈ 𝒢 determines the effective coordinate by projection, G₀ = Ĝ · 𝐗_GT, while the externally observed sector is obtained by imposing the…