A Robustness Analysis of Cosmological Parameter Constraints in the Low-Redshift Pantheon+ Sample Using Tertile Splitting and Redshift-Resolved χ2 Diagnostics

This work investigates the limitations of cosmological parameter inference in low-redshift Type Ia supernova samples, with particular focus on the Pantheon+ dataset. Previous studies have reported the presence of degeneracy-like behavior in the low-redshift subset (z ≤ 0.03639), indicating potential information limitations within this redshift range. To further examine this phenomenon, we employ a position-based tertile splitting scheme by partitioning the low-z subset into three equal-population bins, together with a cumulative redshift-resolved analysis to probe the evolution of cosmological parameters as a function of effective redshift. The results indicate the absence of a well-defined redshift boundary at which inference degeneracy diminishes under the splitting approach. In contrast, the cumulative analysis reveals the presence of distinct regimes characterized by global changes in parameter fitting behavior. The novelty of this work lies in the classification of the Pantheon+ low-redshift sample into information regimes based on cumulative redshift diagnostics, highlighting the necessity of cross-method robustness tests to disentangle data limitations from potential methodological artifacts.