CAD.1:5 - Archetypal Grounding

A constructed actuator model is x_{k+1}=x_k+u_k, with |x|\leq1 and |u|\leq0.06. An existing fast law follows a reference. A planning calculation takes two fast sampling periods on a dedicated resource, so it cannot produce a new result every fast tick. Planning remains useful because it chooses future reference segments; the fast law supplies inexpensive execution.

One candidate sends a new held value every four ticks. Another sends a timed segment whose intermediate values the fast task can generate. They differ in the interaction removed by planning: the first assumes a jump can be tracked within the input limit; the second assumes a known continuous segment and a reliable clock. CAD.2 derives those consequences. Neither candidate has yet earned a safety claim.

As a non-use case, suppose the only task is stabilization around one fixed equilibrium and the existing fast law meets every limit. A slow planner adds no demonstrated decision benefit; keep the simpler controller.