Directional Anisotropy Gravity DAG - Gravity Sector, v10: Paired Directional Channels, Emergent (3+1)-Dimensional Spacetime, Effective Field Theory, Dark Sector, and Galactic Phenomenology

We present a structured effective-theory formulation of Directional Anisotropy Gravity (DAG), an emergent-spacetime framework in which the macroscopic (3+1)-dimensional geometry arises from coarse-graining a discrete oriented substrate whose six primitive directional channels are organised into three pairs of opposite orientations: (f,b), (u,d), and (r,l), each defining one physical spatial axis. Starting from this paired microstructure and an explicit microscopic lattice action, we develop the full theoretical architecture of DAG across five levels: microscopic, kinematic, field-theory, dynamical, and phenomenological. Key results: (1) γ_PPN = 1 follows algebraically from the spatial metric structure; (2) β_PPN = 1 is derived from the trace-reversed (0,0) Ricci equation in the solar-system regime via an algebraic identity for static massless scalars in four dimensions, yielding the closed-form temporal coupling B(Ā) = (1 − ln Ā)²; (3) the asymptotic ρ_M ∝ r⁻² memory-halo profile is derived from the steady-state field equation; (4) 175 SPARC galaxy rotation curves are fitted with median χ²/ν = 1.27; (5) the background expansion history is tested against the DESI DR1 BAO compilation, finding χ²/ν = 1.25 for DAG+memory versus χ²/ν = 1.54 for Planck-2018 ΛCDM (marginal preference, Δχ² ≃ 3.7, not decisive evidence); (6) six explicit falsifiable predictions are formulated. The β_PPN derivation is given in condensed form in Appendix B; the full line-by-line calculation is in the companion technical note (DOI: 10.5281/zenodo.19597452). SPARC fit data are in the companion data record (DOI: 10.5281/zenodo.19404342). v10 adds over v9: β_PPN = 1 derived (not assumed), closed-form B(Ā), and quantitative DESI DR1 BAO test.