In large language models performing long-form reasoning, the KV cache grows rapidly with decode length, creating bottlenecks in memory and inference stability. Existing reasoning-oriented KV compression has mostly followed an eviction-centered view: estimate token importance more accurately, then discard lower-ranked entries. Our analysis suggests that scorer refinement alone often fails to substantially reorganize the actual keep-set and may therefore not be the main lever for preserving reasoning behavior. We instead frame reasoning KV compression as a behavior-preserving structured consolidation problem. CASK partitions the decode-time reasoning trace into a protected core that anchors answer formation and intermediate state, and mergeable scratch with high redundancy. The core is preserved, while selective consolidation is applied only to the scratch. To address prompt-heavy regimes where the prefix can exhaust the budget before decode-stage compression becomes active, CASK further uses a two-stage design: prefix eviction followed by decode-stage consolidation. On the H100 reasoning gate, CASK shows higher full-KV continuation fidelity than TriAttention at matched budgets on both AIME24 and AIME25, with recurring cask@384 > triattention@512 crossings. In prompt-heavy replay, multi_news and vcsum act as decode-active witnesses, while qmsum and gov_report expose the prefix_budget_exhausted boundary. The overall evidence supports a simple conclusion: effective reasoning KV compression depends less on more elaborate scorer engineering than on combining core preservation with selective scratch consolidation to lower the usable budget frontier.