Structured Analysis of Cosmological Inferential Tensions

This technical note presents a structured, diagnostic analysis of the main inferential tensions currently observed in cosmology, including discrepancies related to the H₀ parameter, S₈, large-scale structure measurements, baryon acoustic oscillations, and joint analyses across heterogeneous datasets. The work does not propose new physical models, parameters, or resolutions. Instead, it focuses on identifying and classifying the structural origins of these tensions by explicitly separating statistical variance, conditional structural tension, non-comparability, artificial closure, and failures of global closure. Particular attention is given to the role of comparability, domain of validity, and methodological assumptions in multi-probe analyses. The note emphasizes the diagnostic value of tensions as indicators of regime limits, rather than treating them as anomalies to be eliminated through ad hoc extensions. This contribution is intended as a methodological reference and analytical atlas, supporting careful interpretation of cosmological datasets and clarifying the inferential boundaries within which global fits and consistency claims remain meaningful.