This article presents a critical–propositional analysis of A. J. Maley’s Local Gauge-Invariant Yang–Mills QFT and Vacuum Mass Gap in Four Dimensions for Compact Connected Simple Gauge Groups in confrontation with the Theory of Objectivity (TO). The study examines the paper’s central claims regarding the constructive formulation of four-dimensional pure Yang–Mills theory, the full local gauge-invariant sharp-local operator algebra, and the existence of a positive vacuum mass gap in the Osterwalder–Schrader framework. The article develops its argument by placing Maley’s proposal into dialogue with the foundational bibliography of the Theory of Objectivity, its recent modal and scientific developments, and a broader support bibliography in physics, cosmology, and philosophy of science. Special attention is given to the ontological status of the vacuum, the meaning of gauge-invariant locality, the role of spectral separation, and the distinction between mathematical rigor, physical structure, and ultimate ontological foundation. From the standpoint of the Theory of Objectivity, the study argues that Maley’s work is highly relevant as a model of intramundane structural order, especially in relation to boundary, composition, minimum logical separation, and disciplined relationality. At the same time, it maintains that even a rigorous Yang–Mills construction does not by itself resolve the deeper modal and cosmogonic questions concerning primordial Nothingness, transcendent substance beyond the quantum, and the absolute foundation of the universe. The article therefore proposes a balanced conclusion: Maley’s work may represent a significant contribution to mathematical physics and to the ontology of the quantum vacuum, while the Theory of Objectivity preserves its role as a wider modal framework for interpreting the ultimate conditions of physical intelligibility. An appendix in TO style concludes the paper by reformulating the dialogue in the characteristic conceptual language of the Theory of Objectivity. Keywords:Theory of Objectivity; Yang–Mills theory; mass gap; quantum field theory; gauge invariance; quantum vacuum; Osterwalder–Schrader axioms; Wightman framework; modal ontology; constructive quantum field theory; philosophy of physics; cosmology
Cabannas et al. (Sat,) studied this question.