Strong NP-completeness of interval scheduling with two cancellations and one addition under commitment

Consider weighted interval scheduling in which at most two requests from the entire input may become unavailable after an initial schedule is chosen. Recovery may add at most one available request and must retain every surviving initial commitment. We prove that deciding whether some initial schedule guarantees a specified recovered weight is strongly NP-complete, even for positive integer weights and integer interval endpoints. The reduction starts from a restricted colorful independent-set problem on disjoint paths with at most three vertices. It uses six selectable labels per source vertex and twenty-four guard labels. Positive blockers control unintended recovery; guard attacks exclude every noncanonical initial schedule by an explicit nominal-deficit argument. The proof addresses failures of unselected requests and establishes both directions for the recovered-value threshold itself. Status: research preprint shared for scrutiny. Independent human verification of the complete proof has not been completed; internal AI-agent checks are not human peer review. The manuscript discloses the use of OpenAI Codex and AI agents and describes the human contribution. This record includes the seven-page PDF, its matching LaTeX source and a review/build guide. Comments and corrections are welcome.