Empathy Energy Minimization in the Reasoning Turing Machine

This paper introduces an energy-based coherence principle for reasoning systems within the framework of the Reasoning Turing Machine (RTM). An explicit scalar functional is defined to measure alignment between cognitive inference and valuation pathways, coupled with a contradiction tension term governing epistemic conflict. The resulting total energy serves as a stability functional for continuous-time dynamics, yielding stable attractor states under gradient-based adaptation. The manuscript formalizes internal coherence as a dynamical condition in bounded reasoning systems constrained by computability limits. This work constitutes the first component of a coordinated trilogy. The second paper develops a force-based formulation of behavior emerging from epistemic dynamics, and the third paper extends the framework to long-term consolidation and identity stability under incompleteness constraints.