Qwen2.5-0.5B-Instruct fine-tuned with from-scratch GRPO (Group-Relative Policy Optimization) on the Countdown number-puzzle task — combine the given numbers exactly once with + - * / to hit a target. Rewards are verifiable (exact rational arithmetic via a whitelisted-AST evaluator), so this is RLVR: no reward model, no critic.

This checkpoint is the best ablation (learning rate 3e-6, group 8, 1500 steps).

36x over the base floor (1/300 -> 36/300). Ablations: learning rate was the only lever that moved accuracy (1e-6 -> 3e-6 gave 1% -> 12%); more steps (3000) and larger group (16) both plateaued. Known failure mode: reasoning collapse — the shaped reward scores only the <answer>, so the model emits bare answers with no <think> (format_rate = 0).

Trained for the RLVR Arena capstone (RL in Production Bootcamp).