Phase-Governed Gravity & Dual Projection of the Constraint Geometry Kernel: A Unified Framework

We present a unified framework merging Phase-Governed Gravity (PGG) and the ISL constraint geometry programme. PGG promotes the Randall–Sundrum (RS1) warp factor to a dynamic relaxation field α(x,t) governing vacuum metric coherence — a single move that explains the bifurcation in Ultra-Diffuse Galaxies (Dragonfly 44, NGC 1052-DF2), reproduces SPARC rotation-curve phenomenology without particle dark matter, and recovers Newtonian gravity in clusters. Separately, the ISL constraint geometry programme derives the fine-structure constant α_EM ≈ 1/137 from a 5D kernel K with S₅ symmetry (Φ=120 closure states, η=9 locking channels). We show that the laminar plateau α_lam ≈ 0.35 and α_EM are dual projections of the same kernel K under different operators — neither is a free parameter. Eight explicit falsification criteria and four novel observational predictions are stated, testable by JWST, LISA, and CMB-S4. If the derivation of α_lam from K succeeds without fitting, PGG and the α-derivation program become a single unified geometric result