Four compact classical reading regions

Choose four equally spaced centers

Here the subscript labels a center; it is unrelated to the Cauchy time $s=0$. Choose disjoint small intervals $I_k$ around these centers such that their closures lie in that same positive range. Let the clock history times be

and let $x_A={\chi }^{-1}(0)$.

The history map is

The clock readout occurs later, for example at

Each code will select a compact Ward smearing supported in $I_k\times B_{\rho /4}$, not a point evaluation of a quantum field.