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HyThermal provides a sophisticated framework for treating conceptual relations as dynamic physical systems. By fusing Category Theory (ACSets) with Langevin dynamics, it allows users to perform temperature-controlled exploration of concept spaces, identifying stable clusters and equilibrium distributions. This skill is particularly useful for researchers and developers analyzing complex discussion threads, mapping multi-dimensional knowledge graphs, or optimizing semantic sequences where traditional static graph analysis fails to capture the fluid nature of information flow.