The $H_0$ World Cup. I. Summary of the baseline group stage results

The Hubble tension has reached a nominal significance above $7\sigma$, while new high-precision measurements of the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) sharpen the test of proposed solutions. Using a common framework, we compare fourteen representative alternatives to the standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model in light of up-to-date CMB, BAO and supernovae data to gauge their ability to resolve the tension. The models span late-time modifications, modified recombination, and exotic pre-recombination expansion histories driven by additional radiation or a localized dark energy injection. We evaluate each proposal with complementary frequentist and Bayesian measures of the residual calibration tension and of the improvement in the joint fit. Both approaches identify the same broad hierarchy. Early dark energy and early modified gravity models perform best, shifting the $H_0$ inference without local measurement priors toward $70\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ and reducing the residual discrepancy with SH0ES to approximately $2.5-3.6\sigma$, depending on the model and statistic, while receiving strong support over $\Lambda$CDM in the combined fit. Varying the electron mass at recombination yields an intermediate improvement, whereas the enhanced-radiation and late-time scenarios do not improve over $\Lambda$CDM. This Letter summarizes the group stage of the competition; in a companion paper (Paper II) we present the results of an exhaustive set of analyses and assess their robustness to variations in modeling assumptions and datasets.