Latent chain-of-thought models move intermediate reasoning into continuous states, obscuring which internal object causally carries a computation. We introduce SCIT, the Suffix Cache Interchange Test, which patches exact source–recipient counterfactuals and crosses cache-segment sufficiency with K/V splits, hidden-state and semantic-source controls, decoded validation, and matched corruption. In GPT-2 arithmetic, counterfactual transfer concentrates in value-cache suffix trajectories rather than hidden states, keys, answer slots, or single-token triggers. Full sufficiency-and-necessity closure holds only for the main CODI-GPT2 checkpoint; the Sim-CoT-style reproduction supports sufficiency and decoded transfer but not necessity. Across broader competent cells, arithmetic-like GPT-2/1B tasks retain latent-tail value/KV transfer, whereas 8B and repaired non-arithmetic tasks shift to prompt-prefix or full-cache K/V; ungated cells receive no call. SCIT thus provides a cache-level diagnostic, a checkpoint-specific arithmetic mechanism, and a competence-gated carrier map—not a universal latent-tail claim. Code: https://github.com/YIDING4869/scit-emnlp-2026