Long-context retrieval and agentic workloads repeatedly reuse the same documents under changing instructions, histories, and document orders. Prefix caching cannot exploit this reuse, while position-independent caching (PIC) remains unreliable because independently compiled KV states lack the future context in which they will be consumed. Our diagnostics show that a learned boundary-conditioned baseline sharply reduces attention deviation near reusable-block boundaries but leaves interior and task-level residuals, motivating adaptation of the document representation itself. We present \emph{SemPIC}, which trains a LoRA-enabled Writer to compile native per-layer document KVs through behavioral distillation while retaining the pretrained decoder as an unchanged Reader. Adaptation is confined to offline cache construction, preserving the standard KV interface and cache-hit decoding path. We further introduce KV Gradient Checkpointing, which reduces peak training memory without severing gradients through cached KVs. Across three models and four tasks, SemPIC raises mean micro-F1 over KV Packet from 0.53 to 0.60, approaching Full Recompute at 0.62.

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