Tiered hot-cold storage

Design a tiered hot/warm/cold + archival storage system that automatically moves objects between cost tiers based on access patterns. Constraints: a hot SSD tier (single-digit-ms reads, expensive), a warm HDD tier, a cold/archive tier (minutes-to-hours retrieval, ~10x cheaper), billions of objects, and you must minimize cost while keeping frequently-read objects fast. Cover the tiering engine, access tracking, and retrieval.