Programmable Spectral Computing: Emergence of Modal Execution Logic

We report a structural discovery in frequency-based computing: that frequency- structured modal fields ϕ(t) can be dynamically activated through time-windowed control to produce interpretable logic trajectories. Unlike previous models based on spectral simulation, this framework introduces programmable frequency slot activation, state-driven output modulation, and entropy-based feedback stabiliza- tion. Modal execution is orchestrated by an external instruction structure, enabling the first demonstration of logic behavior in the frequency domain without tradi- tional transistors or digital gates. This work lays the foundation for a new class of post-silicon computing architectures driven by wave-based physics, offering a path toward ultra-low-power, scalable computation.