THE FOUR TENSION GATES AND THE MODAL DISCIPLINE OF OBJECTIVITY: a critical–propositional analysis of Zhai XingYun's PAPER-FBT01B in confrontation with the axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras of the

This article presents a critical–propositional analysis of Zhai XingYun’s PAPER-FBT01B: The Four Tension Gates: Structural Origin, Gate Algebra, and Geometric Roles (v3.9), published on Zenodo with DOI https://doi.org/10.5281/zenodo.20290219, in dialogue with the Theory of Objectivity developed by Vidamor Cabannas and Denivaldo Silva. The study examines the four tension gates , their algebraic organization as , the distinction between horizontal and vertical sectors, the residual central role of the -gate, and the relation between generator-level structures and invariant-level structures within the Fracture–Berry–Tension Framework. These elements are analyzed in confrontation with the modal axioms of the Theory of Objectivity, its phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras. The article argues that Zhai’s FBT01B offers a relevant algebraic–geometric bridge for dialogue with the Theory of Objectivity, especially regarding boundary, observability, structural anteriority, residual phase, and formal differentiation. At the same time, it identifies important theoretical limits, since FBT01B does not begin from Nothingness as a primitive and eternal mathematical essence, does not formulate a complete cosmogony, and does not explicitly identify information, knowledge, and atomic radiation as the transcendent element in the sense proposed by the Theory of Objectivity. This analysis counted on the analytical support of ChatGPT. Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Zhai XingYun; Fracture–Berry–Tension Framework; FBT01B; four tension gates; modal discipline; phenomenic elements; Inducer Effects; cosmogonic theorem; cosmological Eras; structural ontology; symplectic geometry; residual phase; scientific dialogue.