A model can know when two events occurred yet still answer which came first incorrectly. Multi-hop QA accuracy conflates such composition errors with missing facts. We introduce a double-gate protocol for temporal factual chains and evaluate a case for composition only if the model (i) answers every constituent fact correctly across paraphrased probes and (ii) answers every aligned sub-question correctly in isolation. If the original multi-hop answer remains incorrect, the case is a residual composition failure; we call the systematic occurrence of such failures composition collapse. On D4v2, a benchmark of 390 temporal chains, two post-trained models differ by only 0.3 percentage points in atomic stability yet by 47.4 points in depth-2 (two-fact) residual failure. In a controlled same-base comparison, outcome-verified reinforcement learning reduces depth-4 residual failure by 54 points relative to reasoning-trace SFT under matched data and LoRA budget. On 80 examples that pass both gates for every GRPO variant, failure decreases monotonically, showing that model-specific gate subsets are unlikely to drive the trend. Finally, chain-of-thought decoding recovers 70–75% of gate-passing failures, consistent with an important role for inference-time computation. These results motivate reporting atomic stability and gate-controlled composition separately when evaluating multi-hop reasoning.