Since generative artificial intelligence (AI) tools such as OpenAI's ChatGPT became widely available, researchers have used them in the writing process. The consensus of the academic publishing community is that such usage must be declared in the published article. Academ-AI documents examples of suspected undeclared AI usage in the academic literature, discernible primarily due to the appearance in research papers of idiosyncratic verbiage characteristic of large language model (LLM)-based chatbots. This analysis of the first 500 examples collected reveals that the problem is widespread, penetrating the journals and conference proceedings of highly respected publishers. Undeclared AI seems to appear in journals with higher citation metrics and higher article processing charges (APCs), precisely those outlets that should theoretically have the resources and expertise to avoid such oversights. An extremely small minority of cases are corrected post publication, and the corrections are often insufficient to rectify the problem. The 500 examples analyzed here likely represent a small fraction of the undeclared AI present in the academic literature, much of which may be undetectable. Publishers must enforce their policies against undeclared AI usage in cases that are detectable; this is the best defense currently available to the academic publishing community against the proliferation of undisclosed AI.