Spectral Logic Computing via Frequency-Density Phase Transitions in Noncommutative Modal

We demonstrate that noncommutative modal networks (as described in the noncommutative spectral operator model) are not merely capable of approximat- ing Riemann zeta zeros, but can be structurally extended to support programmable spectral logic computing. Through the introduction of frequency-spacing-induced propagation locking, we identify a critical phase boundary that separates active spectral transmission from frozen modal memory. We develop a family of spec- tral logic gates (AND, OR, MUX), controlled entirely through frequency density (√λn spacing), and show how they can be composed into functional logic systems. This work extends the noncommutative spectral operator framework beyond spec- tral reproduction into dynamic logic control, memory encoding, and composable frequency-based computing