A counterexample to an interval-valued alternative theorem and checks on an illustrative optimization example

This independent technical note gives an explicit convex interval-valued counterexample to Theorem 1 of Roy, Joshi, Singh and Hamdi, “Some results on directionally differentiable multicriteria interval-valued optimization problems with vanishing constraints” (JIMO 22(2), 2026, 806–831; DOI: 10.3934/jimo.2026029). It examines the nonzero separate-endpoint KKT interpretation, identifies invalid interval endpoints and failures of convexity in Example 1, and computes the displayed ABCQ inclusion directly. It also records the necessity of excluding zero objective multipliers in sufficiency statements. The note distinguishes disproved statements from dependent proof gaps and possible repairs; it does not claim every downstream theorem is false. Files: revised four-page PDF and a ZIP containing the PDF, LaTeX source, exact arithmetic checks and README. AI disclosure: OpenAI ChatGPT was used for English-language improvement, computational checks, and assistance with mathematical analysis and drafting. The author assumes full responsibility for the construction and verification of counterexamples, proofs, and all mathematical statements.