Mathematical Modeling of High-Order Metacognitive Control in Sustained Vocalization: Free Energy Minimization and Attractor Dynamics via Precise Top-Down Intentionality

Abstract

This paper presents a formal mathematical and computational model of the subjective states of clarity, focused intention, and unwavering conviction experienced during sustained traditional chanting. Extending our previous bio-physical framework of microtubule coherence, we model the brain as a hierarchical predictive processing system operating under the Free Energy Principle (FEP). We propose that the traditional practice of precise intention-setting ("declaration") functions as an operation that establishes a high-precision prior, minimizing internal prediction errors and epistemic uncertainty. Furthermore, we demonstrate how altruistic and ethical constraints serve as a regularization term that suppresses self-referential default-mode network (DMN) noise and amygdala-mediated anxiety. Combined with acoustic-driven neural entrainment, these top-down constraints induce a phase transition toward a stable fixed-point attractor in the state space of prefrontal-subcortical networks, providing a rigorous mathematical basis for the qualia of absolute conviction.