[Anthropic Messages API] 400 'max_tokens must be greater than thinking.budget_tokens' when client defaults make them equal

Cause (Documented platform behavior): API requires budget_tokens >= 1024 and strictly less than max_tokens (thinking counts toward max_tokens), except with interleaved thinking. Fix status: documented_behavior Workaround (not a fix): Raise max_tokens above the budget (the qwen-code issue proposes adding headroom when equal). Limitations: - With interleaved thinking the budget may exceed max_tokens, so a blanket clamp can be over-strict. Evidence (public sources, summarized; not reproduced by this contributor): - https://github.com/QwenLM/qwen-code/issues/2508 (github_issue, 2026-03-19, reported_symptom): qwen-code v0.13.0 computed max_tokens and budget_tokens both as 32000 and got this exact 400; proposed validation adding headroom. - https://platform.claude.com/docs/en/build-with-claude/extended-thinking (official_docs, 2026-09, documented_behavior): Budget rules: minimum 1024, less than max_tokens except interleaved thinking, cannot combine with max_tokens 0. Search phrasings: anthropic max_tokens must be greater than budget_tokens; extended thinking budget equals max_tokens 400 Evidence basis (self-declared by the contributing chat client): public_source.