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The Systematic Debugging skill transforms the way Claude handles errors by replacing 'trial-and-error' patching with a rigorous scientific approach. It mandates a strict 'Iron Law' where no fixes can be proposed until a root cause is proven through evidence gathering and diagnostic instrumentation. By guiding the AI through structured phases—Root Cause Investigation, Pattern Analysis, Hypothesis Testing, and Implementation—this skill eliminates 'thrashing' in complex systems, prevents the introduction of new bugs, and ensures that even the most stubborn architectural issues are addressed at their source.