From Scratch II: An Empirical Test of the Flat-Universe Assumption

This paper evaluates the spatial curvature parameter Ωₖ using only late-time observations (z ≲ 2.5), without invoking early-Universe assumptions such as the sound horizon, recombination physics, or CMB-based priors. Cosmic chronometer measurements are used to reconstruct the expansion history H(z) via Gaussian Process regression, and Monte Carlo propagation is employed to assess curvature sensitivity through distance relations. The analysis shows that late-time data alone constrain Ωₖ only weakly (σ ≈ 0.01), indicating that spatial curvature is not empirically determined by late-time observations. All code and data used in the analysis are publicly available.