Modern KV cache management assumes the chatbot workload: prompts arrive once and the cache grows append-only, so prefix caching and forward-only eviction are correct by construction. Agentic LLMs break this assumption. Their conversations evolve through policy-driven editing: failed tool calls are retried, stale outputs dropped, trajectories pivoted. Two distinct cache problems result. First, identical content moves to new positions between turns, invalidating exact-prefix caches even though the underlying KV would still be valid; recent work on position-independent caching for MLA addresses this reuse problem. Second, and this paper's focus, a policy may need to direct the serving system to actively remove or replace a span of cached content and continue without re-prefilling everything that came after. No existing primitive offers this. Production agentic harnesses fall back to re-prefill on every edit, paying full prefix-recomputation cost; kernel-level eviction methods make their own decisions and cannot accept policy directives from outside the kernel. We introduce Leyline, a serving-side primitive that closes this gap. A declarative directive 4-tuple separates what to edit from how to preserve position correctness. The policy declares the edit and its mode (in-place splice or prefix-trimmed re-prefill for semantic forgetting); an architecture-agnostic interface routes to a per-architecture kernel that restores attention math via a closed-form RoPE-rotation correction. The splice kernel lifts replay cache-hit by +11.2 pp and cuts latency by up to 241 ms. A ten-line truncation rule routed through the same interface lifts agentic solve rate by +14.3 pp on debug-gym. The mechanism is open; the policy space it enables is the agenda.