Supplementary Data for: A Galactic-Cosmic Paradox Resolved How Freeing a Single Parameter in TIS Unified Galactic and Cosmological Scales

Dataset for: The Theory of Information Saturation (TIS) is a theoretical framework aiming to unify the phenomena of dark matter and dark energy. In this work, we present its first comprehensive confrontation with data. We show that the minimal version of TIS, while successfully alleviating the Hubble tension, leads to an internal contradiction: the parameters preferred by cosmology are in strong conflict with the requirements for the existence of solitonic cores in galaxies. Subsequently, we demonstrate that this seemingly fatal paradox is elegantly resolved when the parameter $\alpha$, which governs the shape of the potential, is left free. In this version, the cosmological data themselves prefer a value of $\alpha$ that is fully consistent with galactic scales ($\lambda_C \approx 1.1$ kpc). The final model is statistically preferred over $\Lambda$CDM ($\ln(\mathcal{B}) \approx +2.8$) and resolves both the external Hubble tension (~5.5$\sigma \to$ ~2.5$\sigma$) and the internal galactic-cosmic tension. What appeared to be a flaw became a path to an unexpected concordance.