No Free Parameters --- The Fixed Point Law

We formulate the Fixed Point Law for a reproducing kernel whose geometry is generated by the kernel itself. The central claim is uniqueness: among the kernels admitted by the scalar obstruction, boundary contact, global Bergman, and exterior absorption constraints, exactly one kernel reproduces itself under its induced geometry. That kernel is the Distinguished Reproducing Kernel. The exact branch is encoded by the pair-valued state law

T_K(Σ) = (K, Σ′), K ⊊ Σ, K ⊊ Σ′.

Because the law preserves K, the arena on which T_K has authority is not imported from outside the closure datum. It is generated by K itself: T_K is asserted only on states whose K-sections, boundary residues, and maintained K-substate are admissible for that same kernel. Thus the maintained kernel is preserved inside a richer closed state, but does not exhaust that state. The proof shows that scalar boundary-layer obstruction, boundary contact rigidity, global Bergman rigidity, and admissibility-forced exterior absorption force the Bergman power-law kernel, collapse the radial, contact, kernel-scale, and curvature normalizations into one exact state, and select the canonically normalized complex hyperbolic plane ℂH², hence real dimension four.