Finite clock, residual audit, and encoding limits

Let the clock have dimension $D=2^m$, with orthonormal calibration basis $\{|{\tau }_s⟩{\}}_{s=0}^{D-1}$. Let $S$ denote the surviving finite payload. Apply the basis change taking $|{\tau }_s⟩$ to $|s⟩$, then destructively read all $m$ clock names.