Structural Origin of Cosmological Density Ratios: Ωₘ² = 3Ω_Λ Ωb

This work investigates a simple algebraic relation among cosmological density parameters Ωₘ² ≈ 3\,Ω_Λ\,Ωb suggested by representative late-time cosmological parameter estimates reported by Planck and DESI analyses. We present a minimal structural framework in which the density sector is organized into three phases: an unconstrained component (Ω_Λ), a semi-constrained component (Ωdm), and a fully constrained component (Ωb), with Ωₘ = Ωb + Ωdm. The hierarchy is parameterized by a single structural ratio R = 26/12 = 13/6, which leads to Ω_Λ : Ωₘ : Ωdm : Ωb=3R² : 3R : (3R-1) : 1. After normalization the framework predicts Ω_Λ = 169/247, Ωₘ = 78/247, Ωdm = 66/247, Ωb = 12/247. These values satisfy the quadratic closure relation Ωₘ² = 3\,Ω_Λ\,Ωb and correspond to the closure diagnostic Q = √Ωₘ²/3\,Ω_Λ\,Ωb = 1. Using representative parameter combinations from Planck 2015, Planck 2018, and DESI 2024 cosmological analyses, the inferred values cluster near this predicted closure relation. The results suggest that the cosmological density sector may exhibit a simple structural organization at the level of parameter ratios.