{"id":"integer-arithmetic-avoids-float-precision","text":"Solutions systematically choose integer operations — math.isqrt over math.sqrt, integer division over float division, sum comparison over average comparison — to avoid floating-point precision loss that could produce incorrect results for large inputs.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["isqrt-over-sqrt-for-large-inputs","pivot-integer-isqrt-not-sqrt","sum-substitution-avoids-float-precision","percentage-floor-integer-arithmetic"],"outlist":[],"label":"four independent solutions independently chose integer arithmetic to dodge the same class of bug (float precision near integer boundaries), indicating a deliberate defensive pattern"}],"dependents":["exactness-over-performance-at-every-layer","integer-accumulators-precision-safe"],"metadata":{"last_reviewed":"2026-06-07T22:02:22","review_result":"unnecessary"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"integer-arithmetic-avoids-float-precision","truth_value":"IN","reason":"SL justification valid","antecedents":["isqrt-over-sqrt-for-large-inputs","pivot-integer-isqrt-not-sqrt","sum-substitution-avoids-float-precision","percentage-floor-integer-arithmetic"],"label":"four independent solutions independently chose integer arithmetic to dodge the same class of bug (float precision near integer boundaries), indicating a deliberate defensive pattern"},{"node":"isqrt-over-sqrt-for-large-inputs","truth_value":"IN","reason":"premise"},{"node":"pivot-integer-isqrt-not-sqrt","truth_value":"IN","reason":"premise"},{"node":"sum-substitution-avoids-float-precision","truth_value":"IN","reason":"premise"},{"node":"percentage-floor-integer-arithmetic","truth_value":"IN","reason":"premise"}]}}