{"id":"union-by-rank-increments-on-tie-only","text":"Rank is incremented only when merging two roots of equal rank, maintaining it as an upper bound on subtree height.","truth_value":"IN","source":"entries/2026/06/06/find-if-path-exists-in-graph-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"union-by-rank-increments-on-tie-only","truth_value":"IN","reason":"premise"}]}}