Fixed-depth recurrent GRPO

Use the Nanbeige recipe with --algorithm grpo, or invoke examples/looped_grpo/run.py with the same model/data/revision/output arguments. The launcher shares the recurrent training entry.

GRPO trains an actor with VIME’s existing clipped policy loss and per-prompt reward normalization. Defaults use four prompts with four completions each. Group size must be at least two. Complete, ordered groups are checked before math reward calculation; each completion keeps its seed, fixed-depth trace and policy identity. No additional batch-wide advantage whitening is applied. Equal rewards within a group yield zero advantages and may leave policy weights unchanged.

Fresh resume restores only checkpoints/actor, the dataset cursor and sample indices, then publishes the full actor before generating. Compare tokens, rewards, traces and actor/optimizer/scheduler/RNG state with uninterrupted training.