The Complete Constraint Structure of Cosmological Fine-Tuning: Θₚ as the Necessary Admissible Region and the Constraint Coupling Prediction

This paper proves that the admissible parameter region Θₚ is exactly the intersection of the structural constraints derived in Papers 106–108: Θₚ = CM ∩ CKF ∩ CKR. Fine-Tuning is the parameter-space projection of this intersection. This paper additionally identifies a non-obvious structural prediction: the Constraint Coupling Prediction. Because the same physical constant can simultaneously affect multiple LP structural variables (α affects both K and F; G affects both K and R), the boundaries of the individual constraint regions are not independent in parameter space. There exist iso-persistence curves — paths through parameter space along which compensatory variations keep θ ∈ Θₚ. This structural coupling between constraint dimensions is a prediction of the intersection structure of Θₚ that has no equivalent in standard Fine-Tuning accounts, which treat each constant's range as independently determined.