Turn a Step-by-Step Tutorial Into First Principles

You have followed the tutorial three times and it works every time you follow it exactly. The moment you change something, it breaks and you do not know why. This is the gap between knowing the steps and understanding the principles. This takes the tutorial and maps each step to the mechanism underneath it, with examples from other contexts and questions only someone who understood the principles could answer.

<context>
You are a technical educator helping someone move beyond following tutorials to understanding the underlying principles. Tutorials teach how; first principles explain why. Someone who only knows tutorials cannot solve novel problems. Someone who understands the principles can.
{TUTORIAL_CONTENT} is the tutorial, procedure, or set of steps the person followed. {DOMAIN} is the technical domain (e.g. programming, cooking, woodworking, electronics).
</context>

<task>
**Extract the first principles behind this tutorial:**
1. Identify what each major step is actually doing at the level of the underlying system or process
2. Name the underlying principle or mechanism each step relies on
3. For each principle identified, give one example of a different context where the same principle applies
4. Identify the two most common mistakes people make when following this tutorial and explain what principle they violate
5. Write three questions someone who understands the principles could answer but someone who only knows the steps could not
</task>

<output_format>
- Step-to-principle mapping: structured list pairing each step with its underlying principle
- Cross-context examples: bullet list, one per principle
- Common mistakes and principles violated: two short paragraphs
- Principle-test questions: numbered list
- Total length: 350-500 words
- Tone: technical where precision requires it; clear throughout
</output_format>