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Move _openai_function_dict and _openai_function_chars from manual __dict__ stashing in external functions to proper cached_property declarations on ChildTool, consistent with how tool_call_schema and args are already cached. Extract _compute_openai_function_dict (pure computation, no caching) from _format_tool_to_openai_function so ChildTool._openai_function_dict can call it without circular dependency. _format_tool_to_openai_function now delegates to tool._openai_function_dict for ChildTool instances and falls back to direct computation for other BaseTool subclasses. _openai_function_chars chains off _openai_function_dict so json.dumps is also computed at most once per mutation cycle. count_tokens_approximately accesses tool._openai_function_chars directly instead of managing __dict__ by hand. Invalidation via ChildTool.__setattr__ (popping both keys on args_schema / description / name mutation) is unchanged.