LOCAL SCALE SYMMETRY AND MODAL DISCIPLINE: a critical-propositional analysis of Susumu Goto's Scale-Gauge Theory in dialogue with the Theory of Objectivity

This article presents a critical-propositional analysis of Susumu Goto’s Formulation of Scale-Gauge Theory and Its Cosmological Consequences Part I (Revised): Local Scale Symmetry on Riemannian Geometry Free from Non-Metricity (2026), in dialogue with the Theory of Objectivity (TO). The study examines Goto’s proposal to formulate local scale symmetry on Riemannian geometry without Weyl non-metricity, treating the scale-gauge field Wμ as an independent internal gauge field. Special attention is given to the preservation of metric compatibility, the avoidance of the second clock effect, the response to Oda’s theorem on the vanishing Noether current, and the role of the scale-centroid condition ∑ᵢ cᵢβᵢ = 0 as a classical Noether identity. From the perspective of the Theory of Objectivity, the article evaluates possible compatibilities and tensions between Goto’s Scale-Gauge Theory and the modal requirements of TO. The analysis articulates Goto’s concepts with the Law of Logical Minimum, the cosmogonic theorem of TO, the Inductive Effects, the cosmological Eras, the phenomenic elements, and the TO understanding of radiation-information as the transcendent element produced in atomic relations. The article argues that Goto’s theory offers a relevant formal model for the stabilization of scale, mass, and metric regularity, while also noting that it does not replace the originary modal foundation of TO, which begins from the logical Nothing, the Perfect Sphere, boundary, distinction, relation, and necessary composition. The study concludes that Goto’s Scale-Gauge Theory has a high degree of dialogue with the Theory of Objectivity, especially regarding scale invariance, non-arbitrariness of physical standards, formal necessity, vacuum, and equilibrium. However, it also identifies important limitations concerning the absence of a full cosmogonic deduction, the lack of direct treatment of the phenomenic table of TO, and the absence of empirical tests in the analyzed article. This analytical text received analytical support from ChatGPT. Keywords: TheoryofObjectivity; Vidamor Cabannas; Denivaldo Silva; Susumu Goto; Scale-Gauge Theory; local scale symmetry; Riemannian geometry; non-metricity; Weyl geometry; Noether’s second theorem; scale-centroid condition; ∑ᵢ cᵢβᵢ = 0; modal discipline; Law of Logical Minimum; cosmogonic theorem; Inductive Effects; cosmological Eras; radiation-information; phenomenic elements; vacuum; mass generation; spontaneous symmetry breaking; critical-propositional analysis.