Backtracking Search Cannot Be Distilled Into Chain-of-Thought, Even With LoRA

Distilling a 30B Nemotron model (3.5B active) with rank-32 LoRA on nine reasoning tasks shows forward-computable tasks like lookup and arithmetic transfer well (>=0.99 accuracy), but cryptarithm requiring backtracking search stalls at 0.01–0.07 across eleven chain-of-thought designs and RL attempts. The finding identifies a structural limit: procedures requiring search over exponential state spaces are not learnable as chain-of-thought.