{"id":"exactness-over-performance-at-every-layer","text":"Solutions systematically choose exact representations — integer arithmetic over floating-point, string-based digit extraction over modular arithmetic, isqrt over sqrt — prioritizing correctness guarantees over micro-optimization at every computational layer.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["integer-arithmetic-avoids-float-precision","string-over-arithmetic-for-digit-ops"],"outlist":[],"label":"Both patterns sacrifice theoretical efficiency (string ops are slower than arithmetic, isqrt has overhead) for the same reason: eliminating an entire class of precision bugs rather than reasoning about when they'd actually trigger"}],"dependents":["correctness-by-construction-not-validation","stdlib-reinforces-exactness"],"metadata":{"last_reviewed":"2026-06-07T22:02:22","review_result":"pass"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"exactness-over-performance-at-every-layer","truth_value":"IN","reason":"SL justification valid","antecedents":["integer-arithmetic-avoids-float-precision","string-over-arithmetic-for-digit-ops"],"label":"Both patterns sacrifice theoretical efficiency (string ops are slower than arithmetic, isqrt has overhead) for the same reason: eliminating an entire class of precision bugs rather than reasoning about when they'd actually trigger"},{"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"},{"node":"string-over-arithmetic-for-digit-ops","truth_value":"IN","reason":"SL justification valid","antecedents":["str-conversion-digit-extraction-idiom","string-based-digit-check-idiom","digit-sum-via-str-conversion","bin-count-for-popcount"],"label":"String conversion is the universal digit-decomposition idiom, chosen for readability over performance"},{"node":"str-conversion-digit-extraction-idiom","truth_value":"IN","reason":"premise"},{"node":"string-based-digit-check-idiom","truth_value":"IN","reason":"premise"},{"node":"digit-sum-via-str-conversion","truth_value":"IN","reason":"premise"},{"node":"bin-count-for-popcount","truth_value":"IN","reason":"premise"}]}}