Stellar classification has traditionally relied on discrete categories, despite stellar evolution being a fundamentally continuous process. This mismatch limits our ability to measure similarity between stars in a principled way. This work introduces the Star-States Kernel, a mathematically grounded framework for defining similarity between stars represented as vectors of physical parameters. In the context of machine learning, a kernel is a function that encodes similarity while enabling geometric analysis in high-dimensional spaces. Unlike standard kernels, the Star-States Kernel is constructed directly from astrophysical observables and is designed to reflect the geometry of the Hertzsprung–Russell diagram and stellar evolution. The framework enables continuous comparison of stellar configurations, supports kernel-based modeling approaches such as Gaussian processes, and provides a new geometric perspective on stellar populations and evolutionary tracks. This work is theoretical in nature; several extensions remain unproven, and empirical validation using large stellar surveys is identified as future work.