14.1 What the comparison does and does not require
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The suffix need not reverse the prefix. Output feedback and a target direction distributed among many registers are permitted. Only boundary correctness and reversibility are used. Equivalently,
\[
f(x)=1\quad\Longleftrightarrow\quad P(x,0)\ne Q^{-1}(x,0).
\]
This is a necessary representation, not a circuit lower bound from packet count. Expanded monomial counts, individual degrees, and algebra dimensions remain distinct from the shared cost of constructing the complete family. The declared finite cut checks are reported in Section E.4.