This article presents a critical-propositional analysis of Eckhard Hitzer, Manos Kamarianakis, George Papagiannakis, and Petr Vašík’s “Survey of New Applications of Geometric Algebra,” published in Mathematical Methods in the Applied Sciences and associated with a Zenodo record. The study examines the relevance of Clifford geometric algebra as a formal and operational language for representing relations, boundaries, transformations, orientations, fields, signals, and multivectorial compositions. The analysis confronts the surveyed applications of geometric algebra with the Theory of Objectivity (TO), especially its modal axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras. It argues that geometric algebra does not constitute a cosmological theory and does not replace the modal-ontological foundation of TO. Nevertheless, it may serve as a powerful auxiliary language for the future formalization of TO, particularly in relation to boundary, recursive composition, logical tracks, triadic observation, convergence zones, and information/radiation structures. The article also considers the TO interpretation according to which the transcendent element is knowledge or information produced in atomic relations and equivalent to atomic radiations. In this sense, the analyzed work is read as an important methodological bridge between TO and contemporary mathematical physics, information theory, signal processing, artificial intelligence, robotics, and applied geometry. This analytical text received analytical support from ChatGPT. Keywords: Teoria da Objetividade; Vidamor Cabannas; Denivaldo Silva; Theory of Objectivity; geometric algebra; Clifford algebra; Eckhard Hitzer; Manos Kamarianakis; George Papagiannakis; Petr Vašík; modal ontology; cosmology; boundary; recursive composition; Inducer Effects; phenomenic elements; atomic radiation; information; mathematical formalization; artificial intelligence; contemporary physics.
Cabannas et al. (Thu,) studied this question.