MECHANICAL GEOMETRY, ACCELERATION, AND THE MODAL DISCIPLINE OF OBJECTIVITY: A critical–propositional analysis of Zhang Xuan's pulled-out triangle model in confrontation with the axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras of the Theory of Objectivity

This article presents a critical–propositional analysis of Zhang Xuan’s From the Pulled-Out Triangle to the Decomposition of Velocity: The Discovery of a Mechanical-Geometric Model (Zenodo, 2026, DOI: https://doi.org/10.5281/zenodo.20185322) in dialogue with the Theory of Objectivity (TO). The analyzed work proposes a mechanical-geometric model inspired by Ernst Mach, in which a right triangle pulled out from behind a baffle is used to derive relations among incremental velocity, time, acceleration, and velocity decomposition.

The analysis examines possible compatibilities and tensions between Zhang Xuan’s model and the modal axioms of the Theory of Objectivity, especially regarding boundary, composition, relational observation, phenomenic elements, Inducer Effects, the cosmogonic theorem, and the cosmological Eras of TO. Particular attention is given to the model’s equations t = c/u, a = u/t, a = u²/c, and v = √(v₀² + u²), interpreted as operational bridges for the geometrization of kinematic relations.

The article argues that Zhang Xuan’s proposal offers a relevant local and operational bridge between geometry and physical intelligibility, especially in relation to the TO themes of boundary, relational constitution, and the composition of elements. However, it also emphasizes that the model does not replace the full cosmogonic theorem of the Theory of Objectivity, since it does not address the origin of the universe, the Antagonistic Tempus, the informational transcendent element, atomic radiations as knowledge produced in atomic relations, or the complete cosmological Eras of TO.

This analysis counted on the analytical support of ChatGPT.

Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva;  Zhang Xuan; mechanical-geometric model; acceleration; velocity decomposition; Ernst Mach; t = c/u; a = u/t; a = u²/c; v = √(v₀² + u²); modal axioms; phenomenic elements; Inducer Effects; cosmogonic theorem; cosmological Eras; operational geometry; boundary; physical intelligibility; kinematics; Zenodo.