The authors thank the associate editor and two anonymous reviewers for their thoughtful comments and constructive suggestions, which substantially improved both the exposition and technical presentation of this paper. The authors thank Dmytro Perepølkin for his feedback on an early draft of this paper. The authors are grateful to Tom Keelin for comments on an earlier draft that helped clarify the distinctions between the design philosophies underlying the Metalog and QFlex systems. The authors also thank Lonnie Chrisman for insightful discussions regarding QFlex modality and the rank properties of the QFlex design matrix, which helped sharpen the presentation of Theorem 3, and Rohit Khanna for his careful numerical investigations related to Theorem 3 and QFlex modality. Portions of this manuscript were prepared with the assistance of OpenAI’s ChatGPT (v5.2) to support grammar refinement, organizational editing, wording suggestions, and the generation of alternative phrasings. ChatGPT was used to check mathematical consistency, suggest notation, test exploratory ideas, confirm mathematical derivations, and assist with high-order derivative derivations and tedious algebraic simplifications. All mathematical definitions, derivations, analytical results, numerical experiments, and substantive scientific content were conceived, developed, and verified by the authors. The authors reviewed, edited, and approved all text produced with AI assistance and bear full responsibility for the content of this paper.