{"id":"circular-distance-idiom-min-diff-n-minus-diff","text":"The `min(diff, N - diff)` idiom for shortest arc on a modular ring appears across multiple solutions including `minimum-time-to-type-word-using-special-typewriter`, `distance-between-bus-stops`, and (without wrap) `single-row-keyboard`.","truth_value":"IN","source":"entries/2026/06/06/minimum-time-to-type-word-using-special-typewriter-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":["modular-arithmetic-eliminates-simulation"],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"circular-distance-idiom-min-diff-n-minus-diff","truth_value":"IN","reason":"premise"}]}}