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Apply first principles thinking to break problems down to fundamental truths and reason up from there.
Passed 16 of 22 test cases with the skill, and 9 of 22 without it.
and 9 more in the full report
8 fixed8 passed either way5 still failing1 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 8 test cases the skill fixed. Same model, same prompt, with and without the skill.
Our engineering leadership believes our cloud infrastructure bill will always scale linearly with traffic and that $50,000 per month is the baseline cost for running our streaming service. I want to challenge this thinking. Could you perform a fundamental analysis on this problem? Please state the baseline assumption, provide a breakdown table comparing true physical limits against operational choices for each component, summarize the remaining fundamental facts, reason upward from those facts, and propose an alternative solution.
| Checked | Without skill | With skill |
|---|---|---|
| Includes a 3-column decomposition table with headers Component, Cost/Fact, and Physics or Convention. | Missed | Passed |
| Classifies commercial cloud vendor margin or pricing models as convention rather than physical constraints. | Passed | Passed |
The instructions your model reads when the skill loads.
IRON LAW: Assumptions Are Not Facts
Most "constraints" are assumed, not physical. "We can't do X" usually means
"We haven't seen anyone do X" or "The current method doesn't allow X."
First principles thinking distinguishes between:
- Physical laws (actual constraints: gravity, thermodynamics)
- Conventions (assumed constraints: "this is how it's done")
1. Identify the assumption: What do "everyone knows" or "everyone does"?
2. Break it down to fundamentals: What are the basic, irreducible facts?
3. Reason up from fundamentals: Given only the base facts, what's the best solution?
→ Fundamental constraint found: the COGS includes an unexamined supplier relationship, not a physical constraint.
test cases passed, vs 9 / 22 without
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