La Profilée - Constraints in Standard Cosmology: The Cosmological Constant as a Persistence Bound in ΛCDM

This paper provides the first explicit bridge between the structural persistence law of La Profílée and a standard cosmological fine-tuning result. Building on Paper 104, it shows that in ΛCDM cosmology the cosmological constant Λ functions as a Level-1 parameter that constrains K, the cross-scale integration condition. The standard upper bound on Λ is a persistence bound. This paper additionally develops a quantitative toy model for the K-Erosion Hierarchy — the structurally determined order in which cosmological scales lose K-admissibility as Λ increases. The model derives Kₑff (ℓ, Λ) from linear structure formation theory and shows that ΛK (ℓ) ∝ ℓ^ (−2. 22): larger scales lose K-admissibility at smaller Λ values. This is a falsifiable, scale-specific prediction absent from standard Fine-Tuning accounts.