The four, one, zero illustration separates dependency completeness from answer accuracy carefully. For an empirical follow-up, I would compare a cold computation and an eligible prefix-cache hit using the same token sequence, then inspect next-token distributions before comparing whole generated answers.

A deterministic decode can remain identical despite a measurable distribution shift, while sampling can diverge for reasons unrelated to replay. Recording cache eligibility and the reused-prefix length would keep those conditions distinct. That would test the approximation's practical effect without turning the local ancestry diagram into an unmeasured claim about an agent forgetting its instruction.