= Nonadaptive Clifford measurement pattern
A path <graph state> simulates a sequence of <Clifford gates> $J(\alpha_j)$, $\alpha_j\in\{0,\pi/2\}$, using fixed <equatorial qubit measurement> bases on successive path <vertices>. Let $s_j$ be raw outcomes, $t_j=2\alpha_j/\pi\in\{0,1\}$, and start the <Pauli frame> at $a_0=b_0=0$. Matrix commutation and $J(-\pi/2)=XJ(\pi/2)$ give
$$
a_j=s_j\oplus b_{j-1}\oplus t_ja_{j-1},\qquad b_j=a_{j-1}.
$$
Induction shows the final unmeasured state differs from the ideal circuit output by $X^{a_m}Z^{b_m}$, up to <global phase>. A final <computational basis> result $d$ is corrected to $d\oplus a_m$. All bases are fixed, and projectors on distinct <vertices> commute, so all measurements, including the final one, can occur in a single layer. The frame recurrence is classical outcome processing, not quantum feed-forward.
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