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This paper studies what an SOTM can achieve under two oracle-response schemes: in a cached-response oracle, each distinct query receives one response that is reused on later calls to the same query, while in a fresh-response oracle, each call returns an independent response. In both schemes, the SOTM first computes from its input and internal random source to generate its first query, then proceeds adaptively, computing from its query-response transcript (the record of queries issued and responses received) to generate each subsequent query or produce a final output. 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