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) γPPN = 1 follows algebraically from the spatial metric structure; (2) βPPN = 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 ρM ∝ 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 βPPN 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: βPPN = 1 derived (not assumed), closed-form B (Ā), and quantitative DESI DR1 BAO test.