S₈ as an Interface-Dependent Stress Test: Residual Migration and Asymmetric Closure Across ACT and BAO

This technical note presents a controlled interface-dependent stress test of the clustering amplitude parameter S₈ using ACT DR6 CMB lensing and BAO likelihoods. Rather than proposing resolutions to the S₈ tension or introducing new physical mechanisms, the analysis is explicitly diagnostic. By imposing constrained S₈ priors and tracking the redistribution of χ² contributions across observational interfaces, the study probes whether local consistency can coexist with the failure of global closure. The results show that S₈ behaves differently from H₀ under comparable stress conditions: residuals migrate asymmetrically between interfaces, and no single configuration achieves simultaneous closure across all likelihood components. These findings support an interpretation of cosmological tensions as interface-dependent stress tests rather than indicators of missing parameters or new physics, and contribute to a structured diagnostic analysis of inferential limits in contemporary cosmology.