How I cut my multi-turn LLM API costs by 90% (O(N ) O(N))

How I cut my multi-turn LLM API costs by 90% (O(N²) → O(N)) If you build multi-turn AI agents, you know the pain: API costs don't grow linearly, they grow quadratically. Every turn in a standard agent loop replays the full conversation history. Token cost on turn N is proportional to N , so total cost across N turns is Θ(N²) . I hit a wall where a single heavy day of coding consumed 97% of my weekly Anthropic quota. So I built Burnless — an open protocol and orchestration layer that flips the co