An Independent Billing Audit of Claude's Production API: 4 Experiments Across Haiku, Sonnet, and Opus Confirm Mathematical Honesty; Tool-Definition Overhead and Silent Desktop-App Routing Remain Consumer Concerns

I run an independent inspection of Claude's production billing API across four controlled experiments using Anthropic's free count_tokens endpoint as ground truth.

Findings (all four experiments):

(1) Hidden-overhead probe across 50–15,000 token prompts: zero delta on every sample. No hidden padding.

(2) Tool-definition inflation: a single tool adds 571 extra input tokens; 20 tools add 1,996 per request. Large but fully reported, undocumented in public pricing.

(3) Cache accounting: 2,052-token cacheable prefix written on call 1 reports as exactly 2,052 cache_read tokens on call 2. Write-to-read ratio 1.0000.

(4) Extended-thinking transparency: reported output_tokens matches visible thinking + text content within tokenizer granularity. No invisible reasoning tokens billed.

Conclusion: API-level billing arithmetic is honest. Two consumer concerns survive: (a) undocumented tool-definition overhead, (b) silent routing of subscription users to pay-as-you-go API billing via the desktop app's automatically-created 'coworking' API key (this author personally lost USD $89.90 over 18 days while holding paid Max). Neither is a math issue; both are transparency/consent issues.

Open data + script: https://github.com/norika1207-lab/mercury-paper-handoff