{"id":"closed-form-preferred-over-simulation","text":"When a mathematical closed-form exists (e.g., triangular number formula for arranging-coins), the repo uses it with exact integer arithmetic (`math.isqrt`) rather than iterative simulation or binary search.","truth_value":"IN","source":"entries/2026/06/06/arranging-coins-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"closed-form-preferred-over-simulation","truth_value":"IN","reason":"premise"}]}}