THE GEOMETRY OF EMERGENT DIMENSIONALITY: a critical–propositional analysis of Zhai XingYun's PAPER-DCQ2 in confrontation with the Theory of Objectivity

This article presents a critical–propositional analysis of Zhai XingYun’s PAPER-DCQ2: Emergent Dimensionality, Phase–Orbit Geometry, and Morse–Thimble Convergence via Phase–Encoded Embedding of Binary Configuration Space into Gr(3,6), in confrontation with the Theory of Objectivity developed by Vidamor Cabannas and Denivaldo Silva. The analysis examines how PAPER-DCQ2 proposes a pre-dynamical mathematical architecture in which the six-bit binary configuration space is phase-encoded into the complex Grassmannian , giving rise to the phase-orbit submanifold , quantized Berry curvature with Chern numbers , an effective four-dimensional configuration space , and a Morse–thimble structure with 64 non-degenerate minima corresponding to discrete code states. From the perspective of the Theory of Objectivity, the article interprets DCQ2 as a promising mathematical interlocutor for the problem of how discreteness, phase relations, curvature, topological invariants, and stabilization may contribute to the emergence of objective dimensionality. The discussion articulates possible compatibilities with the Seven Absolute Truths of the TO, the phenomenic elements, the Inductive Effects, the cosmogonic theorem, and the cosmological Eras of the Theory of Objectivity. Special attention is given to the TO thesis that the transcendent element is the knowledge or information produced in atomic relations and equivalent to atomic radiation. In this light, the article proposes that Berry curvature, holonomy, and phase-geometric information in DCQ2 may be read as a formal analogue of relational transcendent information, while also emphasizing the need for modal grounding and empirical operationalization. This analytical text received analytical support from ChatGPT. Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Zhai XingYun; PAPER-DCQ2; discrete–continuous–quantum correspondence; Grassmannian ; emergent dimensionality; phase-orbit geometry; Berry curvature; Chern numbers; Morse theory; Lefschetz thimbles; phenomenic elements; Inductive Effects; modal ontology; cosmogony; transcendent information; atomic radiation; critical–propositional analysis.