The new ChatGPT "study mode" feature appears to be entirely implemented as a carefully crafted system prompt - thankfully OpenAI mostly don't take measures to protect those these days so it's easy to extract it and see how it works
OpenAI
OpenAI30.7.2025
As ChatGPT becomes a go-to tool for students, we’re committed to ensuring it fosters deeper understanding and learning. Introducing study mode in ChatGPT — a learning experience that helps you work through problems step-by-step instead of just getting an answer.
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