Answer Interfaces Change the Measured Cost of Early Stopping

Early-exit methods are commonly compared by reasoning tokens saved and accuracy lost, as if the loss belonged to the stopping rule. Yet a stop returns a reasoning prefix; a terminal interface must still turn it into a scored answer. We hold rule-selected prefixes fixed and cross the interfaces that read them. On Qwen3.5-9B, the same Answer Convergence (AC) stops lose $35.5$ accuracy points under a staged cascade inside the open thinking block and $7.0$ after model-specific closure. Stopping changes how often the answer stage sees an open, unresolved prefix, while requests, prefills and closed generation respond differently to that state. At matched mean reasoning length and a 1K answer allowance, AC trails a fixed-token cut by $9.5$ points under the cascade but leads by $8.0$ after closure. In matched-prefix controls, two closed readouts agree within a pre-specified margin at 2K. The dependence recurs across caps, tasks and checkpoints, while the response to closure and prefill differs across model families. We therefore report complete systems under their own procedures and compare rules conditionally on a specified answer interface.