Abstract
The recent discovery of high-[Formula: see text] superconductivity in hydrogen-rich materials has driven significant progress in superconductor research, particularly in binary and ternary hydrides. However, more complex hydrogen-rich systems remain largely unexplored. Our analysis suggests that while quaternary hydrides adhere to key design principles identified in simpler systems, their distribution within the relevant chemical space is notably sparse, underscoring the need for targeted investigations. By applying stringent selection criteria based on hydrogen fraction, mass ratio, and electronegativity, we systematically reduce the initial database of 38,517,336 possible quaternary hydrides to 1,060,019 promising candidates, representing just 2.75% of the total compositional space. This focused approach enhances the efficiency of computational screening and experimental validation by prioritizing materials with the highest likelihood of exhibiting superconductivity. The results provide a well-defined framework for the discovery of next-generation superconductors, guiding both theoretical exploration and experimental synthesis.