Comparability and Global-Closure Stress Tests in Contemporary Cosmology: A Diagnostic Perspective on Persistent Tensions

Modern cosmology combines heterogeneous observational probes that span different physical regimes, redshift ranges, and inference pipelines. While this integration has enabled remarkable precision, it has also revealed persistent tensions among independent observables, most notably in late-time expansion and structure growth parameters. This technical note presents a set of comparability and global-closure stress tests designed to assess the ability of standard cosmological models and conservative extensions to coherently account for multiple observational channels simultaneously. Rather than proposing new physical components or model modifications, the analysis adopts a diagnostic perspective, focusing on how enforced agreement within selected subsets of observables affects consistency across others. Geometric probes (CMB, BAO, supernovae), growth-related probes (large-scale structure, fσ₈), and integrated probes (gravitational lensing) are examined in terms of their mutual comparability and contribution to global closure. The results show that apparent resolutions of individual discrepancies typically correspond to a redistribution of residual mismatches, rather than a simultaneous improvement across independent observational channels. These findings suggest that persistent cosmological tensions may reflect structural limits in achieving global closure across heterogeneous datasets, highlighting the importance of explicitly testing comparability assumptions alongside continued model and data refinement.