Stage-Replay Divergence Follows the KV Cache: Fixed-Prefix Precision Controls and Bidirectional Cache Transplantation

TL;DR - Identical token prefixes can yield different continuations depending on whether inference reuses a live KV cache or rebuilds it via BF16 prefill. The divergence disappears with FP32, while cache-transplant experiments show that boundary KV state causally determines the divergent trajectory.

• BF16 live-cache versus fresh-prefill runs differed on 166 of 200 suffixes and 20 correctness labels, despite only a one-point accuracy gap.
• FP32 replay produced no decoded disagreements across 200 examples.
• Transplanting all 48 KV layers made continuations follow the donor cache in 24/24 selected cases and 43/43 later replications.
• Exact-token replay can be reproducible without faithfully reconstructing the original decoder state.