6:Tb7c,

Lemma 3.1 (Persistent-stack update). Suppose the old scaffold is strictly backward and satisfies $\mathsf{CleanEmpty}$ . After appending the node specified by the table, the decoded stack at $v^+$ is exactly the result of the selected stack operation. The new scaffold is strictly backward and again satisfies $\mathsf{CleanEmpty}$ .

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