A single flat list of SSTables becomes unmanageable as data grows. The multi-level LSM tree organizes SSTables into levels (L0, L1, L2, ...) with carefully maintained invariants.

Level structure:

• L0 (special): receives direct flushes from MemTable. SSTables may have overlapping key ranges. Reads must check ALL L0 files.
• L1, L2, ... (sorted levels): SSTables within the same level have non-overlapping key ranges. A read only needs to check at most ONE SSTable per level.
• Size ratio: each level is ~10x larger than the previous. L0: 40MB, L1: 400MB, L2: 4GB, L3: 40GB.

Read path (multi-level):

1. Check MemTable (newest data)
2. Check L0 (all files, newest first)
3. Check L1 (binary search by key range, at most 1 file)
4. Check L2, L3, ... until found or exhausted

Request:  {"type": "lsm_level_info", "msg_id": 1}
Response: {"type": "lsm_level_info_ok", "in_reply_to": 1, "levels": [
    {"level": 0, "sstables": 4, "total_bytes": 16777216, "sorted": false, "max_bytes": 41943040},
    {"level": 1, "sstables": 5, "total_bytes": 52428800, "sorted": true, "max_bytes": 419430400},
    {"level": 2, "sstables": 10, "total_bytes": 524288000, "sorted": true, "max_bytes": 4194304000}
]}

Request:  {"type": "lsm_read", "msg_id": 2, "key": "user:42"}
Response: {"type": "lsm_read_ok", "in_reply_to": 2, "value": "Alice", "found_at": "L1", "levels_checked": 2}