The Yang-Mills Mass Gap as a Computational Minimum: A Derivation from the Metric Lag Potential

We propose a novel derivation of the Yang-Mills mass gap from first principles of algorithmic information theory. Building on the framework of Emergent Gravity as a Computational Constraint (Trautwein 2026), we demonstrate that the mass gap Δ > 0 is not an independent postulate of quantum field theory but a necessary consequence of the minimum computational overhead required to maintain a stable information state in the universal manifold. Specifically, we identify the mass gap with the minimum value of the Metric Lag Potential Φ_L — the irreducible processing latency of the computational substrate. A massless stable Yang-Mills excitation would require Φ_L = 0, which we show is physically forbidden in any finite-capacity computational manifold. This provides the first information-theoretic proof concept for the existence of the mass gap, requiring no renormalization group arguments and no lattice approximations. The result is exact, follows from three postulates, and is falsifiable via the Latency Interferometry Experiment (LIE) described in the companion paper.