用Qwen2.5做200组实验：BF16有166处分歧，FP32无分歧；移植48层KV缓存后分歧跟随供体。
该论文在 Qwen2.5 衍生系统上用 200 项配对实验对比保留 live cache 与一次性 prefill。BF16 下两种构造在 166 个后缀和 20 个正确性标签上出现分歧，准确率差 1 个百分点（95% CI [-3.5, +5.5]）。FP32 固定前缀 2x2 对比没有解码分歧（Wilson 95% 上限 1.88%）。跨 48 层 key/value 的双向缓存移植让每个测试分歧跟随缓存供体（24/24 和 43/43）。
Stage-Replay Divergence Follows the KV Cache: Fixed-Prefix Precision Controls and Bidirectional Cache Transplantation
Stage-replay diagnostics reconstruct intermediate token prefixes and treat fresh-prefill continuation as continuation from the decoder state that originally reached the prefix. We audit that assumption at a whole reasoning-stage boundary in a Qwen2.5-derived system. A matched 200-item experiment compares retained live cache with one-shot prefill of identical integer tokens and places an exact replica on both sides. In BF16, replicas remain exact while the constructions differ on 166 suffixes and 20 correctness labels; the accuracy difference is only one point (paired 95% CI [-3.5, +5.5]). A fixed-prefix 2x2 holds all 200 token states constant while crossing construction and precision. The BF16 disagreements recur, whereas FP32 produces no decoded disagreement (95% Wilson upper bound 1.88%). A prospective bridge makes token-by-token incremental and retained live caches bit-exact on 12/12 rows; an all-200 saved-ledger audit reproduces every retained trajectory and comparison fingerprint. Bidirectional transplantation of all 48 key/value layers makes every tested divergent continuation follow its cache donor, both on a selected set at the primary checkpoint (24/24) and an outcome-blind replication at a later checkpoint (43/43). Exact-token replay can therefore be repeatable without preserving live-state fidelity. On the tested states, boundary K/V cache is a causally sufficient carrier of the divergent trajectory, while numerical precision moderates its behavioral expression.