Dynamic Kernel Evolution in the Entropy-Decay Curvature Framework and Its Manifestation in Graphene Transport

This preprint presents a phenomenological framework for non-stationary interaction kernel evolution applied to transport in ultraclean graphene near the Dirac point. The analysis identifies synchronized anomalies across multiple observables within a localized temperature window and interprets them as signatures of evolving interaction-weighting structure. The framework is applied to previously reported experimental measurements of ultraclean graphene near the Dirac point. An effective kernel memory scale is extracted from minimum conductivity and expressed as a dimensionless ratio relative to the Planckian thermal timescale. The resulting ratio decreases monotonically with temperature following a power-law dependence, remaining sub-Planckian across the measured range. This provides a quantitative proxy for the evolution of interaction-weighting structure under varying thermal conditions. The theoretical structure and its empirical interpretation are under active development, and subsequent work will further refine both the formalism and its experimental connections.