Function refine_lebail_with_runtime 

pub fn refine_lebail_with_runtime(
    input: &LeBailInput,
    options: &LeBailOptions,
    checkpoint: Option<&LeBailCheckpoint>,
    runtime: &mut RefinementRuntime<LeBailCheckpoint>,
) -> Result<LeBailResult, LeBailError>

Run fixed-reflection extraction with host-owned cancellation/events/checkpoints.

The runtime should be fresh for a new run. A continuation restores its accepted counter from the supplied checkpoint before numerical work begins.

Errors

Returns LeBailError for invalid input/checkpoint state, non-normal runtime failures, or numerical evaluation failures.