A unique comparison, rather than false equality

The comparison also transports the corresponding ${{\mathcal{J}}_{g_1}}^2$ to ${{\mathcal{J}}_{g_2}}^2$, since it changes neither the metric coefficients nor the leading scalar source.

For an observable $B_1$ on ${\mathrm{Sol}}_1$, its transport is

This need not be the unchanged evaluation formula on ${\mathrm{Sol}}_2$. Proposition prop:memory already detects that distinction.

The map is classical. It does not construct the quantum algebraic cutoff comparison, which requires an admitted product domain and additional locality hypotheses BFR,DF.