P(all in some semicircle)=∑i=1NP(Ei)=N⋅12N−1=N2N−1P(\text{all in some semicircle}) = \sum_{i=1}^{N} P(E_i) = N \cdot \frac{1}{2^{N-1}} = \frac{N}{2^{N-1}}P(all in some semicircle)=∑i=1NP(Ei)=N⋅2N−11=2N−1N
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There's a broader pattern here. External data sources (Shopify, third-party APIs, user input) will always find the exact edge case your infrastructure doesn't handle. They don't do it maliciously. They just don't know (or care) about your CSV pipeline, your column count, your COPY command. They're just sending you the data they have.