A Finite Relational Closure Analysis of Cosmological Data Tensions

This manuscript applies the Finite Relational Closure Framework (FRCF) to current cosmological data tensions as a diagnostic study of finite observational records. Rather than treating cosmological models as primitive ontological commitments, the paper treats \(\Lambda\)CDM, \(w_0w_a\), and several diagnostic variants as candidate closure generators for finite measurement contexts. The study organizes public cosmological data products into a refinement sequence involving FIRAS, Planck, DESI BAO, Pantheon+, and SH0ES. It then compares how different generators behave as additional observational contexts are added. The analysis is intentionally preliminary and is presented as a screening-level closure diagnostic, not as a final likelihood analysis or a replacement for standard cosmological inference. The main result is methodological. The screening analysis suggests that the CMB--BAO--Pantheon+ closure stress and the SH0ES/local-distance-ladder stress may be usefully treated as distinct finite-context closure obstructions. The \(w_0w_a\) generator gives the largest residual reduction through the CMB--BAO--Pantheon+ stage, while the SH0ES refinement introduces an additional local-ladder closure stress. FRCF-specific diagnostic generators, including distance-duality, sound-horizon, redshift--distance drift, and split-closure variants, are not found to provide a preferred replacement in the simple forms tested, but they help identify where closure stress enters the refinement sequence. The manuscript concludes that FRCF may provide a useful framework for studying cosmological tensions as possible failures of finite relational closure across observational contexts, rather than only as global parameter discrepancies.