Four Null Spacetime Theory II: Transport, Gluing and Discrete Curvature: Shared Faces, Holonomy, Spin Structures and Closed Balanced Spacetimes

add the senteces in crete the text for me to copy Four Null Spacetime Theory is a candidate microscopic framework for spacetime in which finite cells are spanned by four balanced lightlike generators. Building on the geometry of a single cell established in Part I, this paper derives how neighboring cells join and how curvature is encoded in their gluing. An oriented shared face uniquely determines the Lorentz transport and fixes the neighboring balanced frame up to reflection. Across the reflected branch, the face transport remains a metric isometry, while the neighboring cell’s own relational clock differs from the transported clock. Primitive hinge deficits occur in integer multiples of (π/3). Under exact balance a cell has no local shape freedom, its tangent space being only Lorentz transformations and scale, and the Regge action reduces to a count of hinges and cells. For the admissible hinges of two to six cells examined here, composing the face transports reproduces the deficit rotation. Under the minimum-angle convention, reflection gluings admit two equally minimal spin lifts. Global spin consistency is formulated as a ( Z_2) cochain equation. We construct closed balanced complexes with the topologies of (S^4) and (S^3× S^1). For the latter, conjectured counting formulas give an asymptotic averaged curvature-to-volume ratio within 2.9% of the corresponding value for a round static universe. This comparison concerns one averaged scalar. The results establish the geometry of balanced gluing; smooth Lorentzian convergence and a dynamical rule that selects gluings remain open.