OSCILLATORY SPACETIME AND THE MODAL DISCIPLINE OF OBJECTIVITY: a critical–propositional analysis of Lorne Velasquez's phase-dependent mechanism for the Hubble tension in confrontation with the Theory of Objectivity

This article presents a critical–propositional analysis of Lorne Velasquez’s 2026 work, A Phase-Dependent Mechanism for the Hubble Tension from Oscillatory Spacetime, with particular attention to the exact Duffing-oscillator treatment of the oscillatory spacetime framework, the replacement of the sinusoidal approximation by Jacobi elliptic functions, and the resulting implications for the Hubble tension, effective dark-energy dynamics, and cosmological phase structure. The analysis examines possible compatibilities and points of tension between Velasquez’s model and the Theory of Objectivity (TO), especially in relation to its modal axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras. Particular emphasis is given to the TO interpretation of phase, field, boundary, causal horizon, oscillation, information, and cosmological expansion as objective relational structures. Within this framework, Velasquez’s article is read as a mathematically relevant contribution to contemporary cosmological modeling, especially because it tests the robustness of an oscillatory spacetime mechanism by replacing the harmonic approximation with an exact Duffing solution. From the perspective of TO, the model opens a productive dialogue with questions concerning modal necessity, cosmic differentiation, boundary formation, phase-induced expansion, and the informational character of physical observables. The analysis also considers the TO principle according to which the transcendent element of the universe is knowledge or information produced in atomic relations and equivalent to atomic radiations. In this sense, Velasquez’s phase-dependent cosmological correction is interpreted as a possible physical-mathematical expression of a deeper informational structure of the universe, although the model itself does not explicitly formulate information as an ontological category. This critical–propositional study was developed in dialogue with the founding bibliography of the Theory of Objectivity, its recent bibliography, and selected supporting works in modern cosmology, physics, philosophy of science, and information-oriented approaches to reality. Analytical Support Note: This analysis counted on the analytical support of ChatGPT. Keywords Theory of Objectivity; Vidamor Cabannas; Lorne Velasquez; Hubble tension; oscillatory spacetime; Duffing oscillator; Jacobi elliptic functions; dark energy; cosmological phase; modal axioms; phenomenic elements; Inducer Effects; cosmogony; cosmological Eras; information; atomic radiation; cosmic expansion; Friedmann equations; phantom dark energy; boundary ontology; contemporary cosmology.