Where does “gaoler” come from?

I need to work through this etymology chain carefully, but I notice there's a fundamental problem: the chain provided doesn't logically connect "gaoler" to its actual origin. The chain given traces Latin -arius → -us → Proto-Italic -os (a suffix evolution), includes Old French -er and Chinese 兒, but doesn't explain how these elements produce the English word "gaoler" (a person who guards a jail). The actual etymology of "gaoler" is: English gaol (from Old French *gaole) + -er (agent suffix). The chain as presented appears corrupted or test data. Since the instruction states "State only what the chain supports. Do not invent dates, cognates, or intermediate steps," and the provided chain doesn't actually support a coherent etymology for "gaoler," I cannot write an accurate sentence following the rules. **I cannot complete this task as instruct

gaoler (English): Alternative spelling of jailer