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I wanted to test this claim with SAT problems. Why SAT? Because solving SAT problems require applying very few rules consistently. The principle stays the same even if you have millions of variables or just a couple. So if you know how to reason properly any SAT instances is solvable given enough time. Also, it's easy to generate completely random SAT problems that make it less likely for LLM to solve the problem based on pure pattern recognition. Therefore, I think it is a good problem type to test whether LLMs can generalize basic rules beyond their training data.
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A Foreword on AGENTS.md#One aspect of agents I hadn’t researched but knew was necessary to getting good results from agents was the concept of the AGENTS.md file: a file which can control specific behaviors of the agents such as code formatting. If the file is present in the project root, the agent will automatically read the file and in theory obey all the rules within. This is analogous to system prompts for normal LLM calls and if you’ve been following my writing, I have an unhealthy addiction to highly nuanced system prompts with additional shenanigans such as ALL CAPS for increased adherence to more important rules (yes, that’s still effective). I could not find a good starting point for a Python-oriented AGENTS.md I liked, so I asked Opus 4.5 to make one: