Does a small amount of post-training on verifiable arithmetic recover more of the APT4 arm's paired digit-probe deficit than math-and-code recovery pretraining does, and does reinforcement learning with a verifiable reward cause less bits-per-byte damage than supervised fine-tuning at the same gain?

A 2 by 3 factorial on the two continued-pretraining arms of Qwen2.5-1.5B after 500M tokens: no post-training, supervised fine-tuning on 5,000 synthetic arithmetic and STEM examples, and GRPO with an exact-match reward, each within 5M tokens. Endpoints: the paired digit probe with a McNemar test; bits per byte on the ten evaluation texts as the forgetting endpoint, with GSM8K problems only as a contamination-decay reference; pass@1 and pass@k on a held-out set written after the models' training data; KL divergence to the policy before post-training; extraction rate; a likelihood-scored arithmetic endpoint. The comparable quantity is the APT4 arm minus the original-tokenizer arm after post-training against the same difference before it.