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.

When retrieved evidence contradicts parametric memory, language models frequently ignore the context and revert to memorized priors—a failure that undermines the purpose of retrieval augmentation. Contrastive decoding amplifies context-conditioned output to suppress parametric bias, but fixed coefficients cannot track changing disagreement, while output-only adaptive coefficients observe only the final prediction distributions. We propose FIDES (Faithful Inference via Deep Evidence Signals), a training-free decoder that combines signals from output distributions, hidden representations, and prediction trajectories to recompute contrastive intervention strength at every step. A matched, formula-verified audit on 128 NQ-Swap pairs shows that conflict raises Opposition by 0.0969 and the resulting coefficient α by 0.0727 at the same answer-prediction position (both p < 10⁻⁴). The audit also finds only a small Shift effect and saturated clipped Noise, clarifying the limits of the mechanism interpretation. Across three benchmarks and six backbones—four primary 7B/8B models and two scaling backbones up to 70B—FIDES achieves the best context fidelity in all 18 settings, outperforming the strongest training-free baseline by +3 to +13 points. At 70B, fidelity reaches 92–94% while F1 reaches 62–63%, showing that multi-depth stepwise contrast can preserve generation utility while improving evidence following.