No Free Parameters --- The Fixed Point Law

The Fixed Point Law is the exact non-projective closure consequence of the Distinguished Reproducing Kernel (DRK). The DRK is the primitive closure datum in which a maintained reproducing kernel K generates a closure transform T_K and is reproduced exactly as the kernel component of the produced state:

T_K(Σ) = (K, Σ′), with K ⊊ Σ ⊊ Σ′.

The maintained kernel is preserved inside both the candidate state and the produced state, but neither state is exhausted by K, and the strict chain forces a genuine produced-state transition. Exact closure then forces an intrinsic first-order boundary absorber. Strictness gives the floor dim_R V_∂ ≥ 1; canonical single-channel admissibility gives the ceiling dim_R V_∂ ≤ 1. The rank-one boundary classification has vertical response V_∂ ≃ Im 𝔽, with dimensions 0, 1, 3, 7 for 𝔽 = ℝ, ℂ, ℍ, 𝕆. The floor and ceiling therefore force dim_R V_∂ = 1, hence 𝔽 = ℂ. The selected field produces a distinguished J_K² = −I, and the native phase-return identity Exp_K(π_K J_K) + I = 0 follows on that branch. Finally, the single absorber exhausts the first complex boundary response: E_∂ = L_R, while dim_C E_∂ = n − 1. Hence n − 1 = 1, so n = 2. The unique exact closure branch is ℂH².