THE MINIMAL THREE-DIMENSIONAL BOUNDARY AND LOGICAL NOTHINGNESS: a critical-propositional analysis of Fumiyoshi Tamura's article in dialogue with the Perfect Sphere of the Theory of Objectivity

This article presents a critical-propositional analysis of Fumiyoshi Tamura’s work, The Structural Necessity of the Minimal Three-Dimensional Closed Boundary from the Minimal Definition of the Universe (2026), in dialogue with the Theory of Objectivity. The analysis examines Tamura’s formal derivation of a minimal three-dimensional closed boundary, obtained through exhaustive enumeration, affine-rank computation, and progressive elimination, resulting in a tetrahedral structure composed of four support points, four faces, and positive volume. The article reformulates the dialogue with the Theory of Objectivity by emphasizing a decisive conceptual distinction: the surface of a sphere is two-dimensional, and the Perfect Sphere of the Theory of Objectivity cannot be treated as a three-dimensional body. In this framework, the Perfect Sphere has no determined logical center, no filling, no inner void, and no physical volume. It is interpreted as logical Nothingness: the minimum logical condition of existence prior to differentiated boundary, interiority, volume, and phenomenic structure. From this perspective, Tamura’s tetrahedral boundary is not identified with the Perfect Sphere of the Theory of Objectivity. Instead, it is interpreted as a later formal structure, already situated within the regime of differentiation, three-dimensionality, closure, and positive volume. The article argues that Tamura’s work has a high degree of compatibility with the Theory of Objectivity at the level of modal discipline, structural necessity, and the Law of the Logical Minimum, while remaining limited in relation to the full cosmogonic framework of the Theory of Objectivity, since it does not address logical Nothingness, the emergence of differentiation, the Inductive Effects, the cosmological eras, phenomenic elements, or information-radiation as a transcendent element. This analytical text received analytical support from ChatGPT. Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Fumiyoshi Tamura; logical Nothingness; Perfect Sphere; two-dimensional surface; three-dimensional boundary; minimal tetrahedron; Law of the Logical Minimum; modal ontology; Inductive Effects; cosmological eras; phenomenic elements; information-radiation; Zenodo.