No Free Parameters --- The Fixed Point Law

We study the primitive law T_K(Sigma) = K. This law is non-projective by definition: the alternative T_K = cK with c not equal to 1 is the failed projective case. We isolate a theorem ladder showing how scalar-only obstruction, single-channel reproduction, rank-one section geometry, local hyperbolicity, and kernel rigidity force the local hyperbolic Bergman class from the primitive law. In that class, the weighted closure fails by a purely scalar obstruction. We compute that obstruction exactly, identify its residue with boundary contact volume, and reformulate the same asymptotics intrinsically using contrast-ball truncations. Since any uncancelled scalar residue produces projective closure, the primitive law forces all normalization channels to collapse into one unified normalization package. A single-channel exterior absorption theorem then forces complex dimension 2, and the same normalization fixes canonical holomorphic sectional curvature -1. Consequently the realized geometry selected by the primitive law is the canonically normalized complex hyperbolic plane CH^2, hence real dimension 4.