The additional classical hypothesis

The baseline symbols $a_0,r_0$ do not themselves prove gauge-invariant physical values. Choosing a compensating number by hand is not a construction of an independently defined charged coefficient.

Conditional classical pre-combination followed by (eq:encoding) gives

The probability is injective in $I_{\mathrm{rel}}$. Hence it preserves exactly an established identity of that combination, not an identity created by readout.