{"id":"apply-ops-two-phase-pattern","text":"`apply-operations-to-an-array` uses a two-phase in-place transformation: Phase 1 (pairwise doubling, left-to-right with sequential dependency) must complete before Phase 2 (zero compaction via write-pointer), and interleaving them produces incorrect results.","truth_value":"IN","source":"entries/2026/06/06/apply-operations-to-an-array-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"apply-ops-two-phase-pattern","truth_value":"IN","reason":"premise"}]}}