This manuscript introduces "Prime Mechanics" and its induced trajectory theory, "Prime Dynamics"—a formal mathematical framework for studying adaptive existence under disturbance, uncertainty, finite resources, and environmental volatility. Operating from the foundational axiom that "reality cannot be canceled," the theory shifts the objective of cognitive and systemic architectures away from reality-replacement and toward reality-optimization. Rather than treating systemic concepts like resilience, preparedness, integrity, and operational clarity as mere motivational abstractions, Prime Mechanics derives them rigorously as admissible structures within viability-preserving dynamical systems. The framework employs constraint theory, optimal control, and operator theory to model disturbance conversion, adaptive policy updates, positional advantage, and controlled optionality (Prime Superposition). The paper provides formal definitions and mathematical proofs for adaptive resilience, noise collapse, and stability margins. Furthermore, it bridges these continuous abstract concepts with executable computational mechanics, featuring appendices on Lyapunov stability, Fredholm failure modes, regularized determinant collapse certificates, and a finite-dimensional numerical simulation layer built in Python/JAX.
Andrew Kim (2026) studied this question.