{"id":"binary-search-variants-share-convergence-structure","text":"All binary search solutions share the same convergence loop structure (narrow [lo, hi] until they meet) but vary along three independent dimensions: what is searched (raw values vs. derived monotonic functions), bias direction (leftmost vs. rightmost match), and post-loop extraction (lo, hi, or result variable).","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["binary-search-on-derived-quantities-pattern","binary-search-on-value-pattern","left-biased-binary-search-pattern","fixed-point-uses-leftmost-binary-search"],"outlist":[],"label":"the four patterns are orthogonal specializations of one template — search-target and bias are independent choices, and recognizing the shared structure reveals that any new binary search problem maps to a point in this 2D design space"}],"dependents":["lookup-abstraction-trio-covers-all-queries","sorted-order-enables-all-efficient-search"],"metadata":{"last_reviewed":"2026-06-07T22:02:22","review_result":"pass"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"binary-search-variants-share-convergence-structure","truth_value":"IN","reason":"SL justification valid","antecedents":["binary-search-on-derived-quantities-pattern","binary-search-on-value-pattern","left-biased-binary-search-pattern","fixed-point-uses-leftmost-binary-search"],"label":"the four patterns are orthogonal specializations of one template — search-target and bias are independent choices, and recognizing the shared structure reveals that any new binary search problem maps to a point in this 2D design space"},{"node":"binary-search-on-derived-quantities-pattern","truth_value":"IN","reason":"premise"},{"node":"binary-search-on-value-pattern","truth_value":"IN","reason":"premise"},{"node":"left-biased-binary-search-pattern","truth_value":"IN","reason":"premise"},{"node":"fixed-point-uses-leftmost-binary-search","truth_value":"IN","reason":"premise"}]}}