Chaos theory’s classical limits—infinite precision, deterministic absolute flows, and the lack of true intrinsic noise integration [1]—are deductively resolved by radically embedding the Finite-Resolution Random Dynamical System (FR-RDS) into the Universal Rough Operator Algebra (UROA). We rigorously demonstrate that finite resolution is not merely an epistemological limitation, but an absolute physical boundary enforced algebraically by the Topological Fractal Brake. Microscopic chaos (characterized by positive Lyapunov exponents) and macroscopic determinism are perfectly and deterministically reconciled through non-commutative 8-Dimensional tensor projections.
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Seonggil Lee (2026) studied this question.
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