SPACETIME SINGULARITY: a critical-propositional reading of Carlos Cesar Aranda's article in confrontation with the Theory of Objectivity

This article presents a critical–propositional examination of Carlos Cesar Aranda’s paper Spacetime Singularity, Singular Bounds and Compactness for Solutions of the Poisson’s Equation in systematic dialogue with the Theory of Objectivity (TO). The study analyzes Aranda’s mathematical treatment of spacetime singularity through Newtonian potentials, compactness, concentration phenomena, and the proposed renormalization of Newtonian gravitation, while confronting these elements with the modal axioms, phenomenic structures, cosmogonic theorem, and cosmological Eras of TO. The paper argues that Aranda’s contribution is relevant as a rigorous local framework for approaching singular regimes, especially in relation to black holes and the scientific intelligibility of extreme gravitational concentration. At the same time, it maintains that such a framework remains ontologically incomplete when evaluated under the modal discipline of the Theory of Objectivity. The article therefore identifies both compatibilities and tensions: compatibilities regarding boundary, composition, and the disciplined treatment of infinity; tensions regarding the absence of a fully relational ontology of existence, the lack of an explicit transcendent-informational dimension, and the persistence of gravitation as a primary explanatory axis rather than a derived emergent regime. The study also articulates the debate with the foundational bibliography of TO, its recent developments on modal ontology, gravity, vacuum, and cosmic origin, and a broader supporting bibliography in physics, cosmology, and philosophy of science. Special attention is given to the interpretation of the transcendent element as knowledge or information produced in atomic relations and equivalent to atomic radiations. This work is intended as a contribution to respectful scientific dialogue between mathematical physics, cosmology, and modal ontology. Authors’ note: This analytical study was developed with the analytical support of ChatGPT. Keywords: Theory of Objectivity; spacetime singularity; Carlos Cesar Aranda; modal ontology; gravitation; black holes; Newtonian potential; compactness; cosmology; phenomenic elements; Inductor Effects; cosmogonic theorem; philosophy of physics; ontology of boundaries.