Metric disagreement: A (0,5), B (3,3), C (8,9), D (9,1). Tie boundary: A (2,5), B (8,5), C (5,9), D (5,1). Coincident cases: A (2,2), B (2,2), C (8,8), D (8,2). A/C are Circle, B/D Square. Changing scenario preserves query and metric; changing prediction or Reset restores the current experiment baseline. Query, metric and scenario changes clear stale explanations.

The two coordinates count equally as numbers. Euclidean compares exact integer squared distances before taking square roots; Manhattan compares integer absolute sums. Equal plotting scales preserve numerical geometry. The straight Euclidean segment or one Manhattan grid route is shown to every nearest case. Zero-distance paths legitimately have zero length. A combined A/B circle/square mark and separate table rows retain coincident identities; the query can overlap them at the same true position.

1-NN assigns the unique nearest reference’s stored class. This lesson withholds a decision for any nonunique minimum, even if the tied labels agree. That explicit policy is not universal: other implementations may choose by order or another declared rule. Identical coordinates with different labels remain tied under both metrics. No known query label or performance evaluation establishes which metric is appropriate for a real task.

The finite 0..10 integer toy excludes k>1 voting, reference editing, learned weights, feature scaling, obstacles, training optimization, class probabilities and automatic metric choice. Different numeric units could change the meaning of equal weights; no physical mixed-unit distance or universal accuracy guarantee is implied.