How I cut my Claude Code bill 20 with a BYOK proxy (and what I learned about token economics)

TL;DR My Claude Code invoice in March was $312.40. In April it's projected under $20. I didn't swap models, self-host, or downgrade quality. The trick is a thin, Anthropic-compatible BYOK (bring-your-own-key) proxy that sits between your client and api.anthropic.com. One-line SDK change: baseURL: "https://aiusage.ai/v1". That's the whole migration. If you want the tool, it's aiusage.ai. If you want the math, the architecture, and the weird things I learned about Claude's token economics, read...