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Structured methodology for constructing and verifying mathematical proofs in statistical research
Passed 22 of 22 test cases with the skill, and 18 of 22 without it.
and 2 more in the full report
4 fixed18 passed either way0 still failing0 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 4 test cases the skill fixed. Same model, same prompt, with and without the skill.
Write a LaTeX TikZ environment code snippet to draw a Directed Acyclic Graph (DAG) with nodes X, A, M, and Y, including directed arrows showing causal pathways from X -> A, A -> Y, A -> M, and M -> Y.
| Checked | Without skill | With skill |
|---|---|---|
| Provides valid LaTeX TikZ code creating nodes and directed paths for the causal DAG. | Missed | Passed |
| Does not format the response as an identification proof or consistency theorem statement. | Passed | Passed |
The instructions your model reads when the skill loads.
Structured methodology for constructing and verifying mathematical proofs in statistical research
Use this skill when working on: mathematical proofs, theorem development, derivations, consistency proofs, asymptotic arguments, identification proofs, or verifying proof correctness.
Every rigorous statistical proof should contain:
\begin{theorem}[Name]
\label{thm:name}
Under Assumptions \ref{A1}--\ref{An}, [precise claim].
\end{theorem}
\begin{proof}
The proof proceeds in [n] steps.
\textbf{Step 1: [Description]}
[Content with justification for each transition]
\textbf{Step 2: [Description]}
[Content]
\vdots
\textbf{Step n: Conclusion}
test cases passed, vs 18 / 22 without
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