DIMENSIONAL SMOOTHING FOUNDATIONS AND THE MODAL DISCIPLINE OF THE THEORY OF OBJECTIVITY: a critical–propositional analysis of the function χ(ζ), dimensional transitions, and singularity boundaries in confrontation with the axioms, Inducer Effects, cosmogonic theorem, and cosmological Eras of TO

This article presents a critical–propositional analysis of Cameron Gattis’s Dimensional Smoothing Foundations: Proofs 1–4 (2025), published on Zenodo, in dialogue with the Theory of Objectivity developed by Vidamor Cabannas and Denivaldo Silva. The study examines Gattis’s proposal of a dimensional smoothing function, χ(ζ), designed to regulate singularities, ultraviolet divergences, and conservation failures across dimensional transitions in General Relativity and Quantum Field Theory. The analysis confronts Gattis’s framework with the modal axioms of the Theory of Objectivity, especially the principles of boundary, distinction, composition, observation, infinity, and transcendent substance. It argues that Gattis’s treatment of singularities as dimensional boundaries offers a relevant technical bridge to the TO, particularly in relation to the Fourth Absolute Truth, the Inducer Effects, the cosmogonic theorem, and the cosmological Eras of the Theory of Objectivity. Special attention is given to the possibility of interpreting χ(ζ) not only as a mathematical regulator of dimensional transitions, but also as a physical–formal operator of boundary, conservation, and informational preservation. In this sense, the article proposes a dialogue between dimensional smoothing and the TO interpretation according to which the transcendent element of the existential universe corresponds to knowledge or information produced in atomic relations, equivalent to atomic radiations. The article concludes that Gattis’s proposal has a high but incomplete degree of dialogue with the Theory of Objectivity, especially because it offers a promising formal language for singularity, boundary, dimensional transition, and radiative regularization, while still lacking a modal foundation, a full ontology of information, and a complete cosmogonic derivation. This analytical text received analytical support from ChatGPT. Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Cameron Gattis; Dimensional Smoothing Foundations; χ(ζ); dimensional transition; singularity; boundary; modal ontology; Inducer Effects; cosmogonic theorem; cosmological Eras; General Relativity; Quantum Field Theory; ultraviolet divergences; Green’s functions; information; atomic radiation; transcendent substance; ChatGPT-assisted analysis.