= Solution
Choose a <Clifford operation> $D$ with $D|0^n\rangle=|\sigma\rangle$ and absorb $D$ into the circuit. Push each subsequent Clifford gate forward through the computation. A computational-basis measurement made after a Clifford prefix $U$ becomes a <Pauli measurement>
$$
Z_j\longmapsto U^\dagger Z_jU
$$
on the initial state, because Clifford conjugation preserves the <Pauli group>. Adaptivity merely makes the next Pauli depend on earlier classical outcomes.
It remains to eliminate the $n$ stabilizer qubits. Maintain their current <stabilizer group>. For a Pauli $P$ to be measured, there are two cases.
* If $P$ commutes with every stabilizer generator, its action on the one-dimensional stabilizer sector reduces to a Pauli operator on the remaining $t$ qubits, possibly with a known sign. Measure that effective Pauli on $|\rho\rangle$.
* If $P$ anticommutes with some stabilizer $S$, its outcome $\lambda\in\{+1,-1\}$ is uniformly random. Sample $\lambda$ for an ordinary measurement, or set $\lambda=+1$ when the original measurement is postselected. The Clifford operator
$$
V_\lambda=\frac{I+\lambda PS}{\sqrt2}
$$
maps the old stabilizer sector into the $\lambda$ eigenspace of $P$. Updating the Clifford frame by $V_\lambda$ removes this measurement while conjugating every later Pauli to another Pauli.
Iterating this procedure leaves an adaptive <Pauli-based computation> on $|\rho\rangle$. The same classical outcomes determine every adaptive choice and final output, so this gives a <weak classical simulation>. Every postselected $Z$ outcome becomes either a fixed classical $+1$ branch or a postselected $+1$ Pauli measurement, as required.
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