A Model-Independent Structural Framework for Describing Localized Deviations in the Late-Time Cosmic Expansion History

This work presents a fully model-independent structural framework for describing localized geometric deviations in the late-time cosmic expansion history, particularly within the intermediate-redshift interval 0.35 < z < 0.55. The approach introduces a retentive descriptive formalism based on two structural quantities, Δψ and Ξ, which provide a neutral mathematical vocabulary for expressing reconstruction-dependent curvature features without imposing physical interpretation or preferring any cosmological model. The framework is compatible with baryon acoustic oscillation analyses, supernova luminosity-distance reconstructions, and non-parametric methods such as Gaussian processes. It does not propose new physics, does not critique existing models, and does not attach statistical significance to any dataset. Its purpose is strictly structural: to offer a minimal, transparent interface for representing geometric aspects of reconstructed expansion histories. A factual and non-interpretive priority statement is included, noting that the formalism was developed independently and prior to the circulation of 2025–2026 reconstruction studies reporting intermediate-redshift features.