WORLDLINE NON-INJECTIVITY: a critical–propositional analysis of Worldline Non-Injectivity as a Necessary and Sufficient Condition for the Emergence of Holographic Spacetime, by Alex De Giuseppe, in confrontation with the Theory of Objectivity

This article presents a critical–propositional analysis of Alex De Giuseppe’s work, Worldline Non-Injectivity as a Necessary and Sufficient Condition for the Emergence of Holographic Spacetime, in dialogue with Vidamor Cabannas’s Theory of Objectivity (TO). The study examines De Giuseppe’s central claim that worldline non-injectivity constitutes the necessary and sufficient condition for the emergence of finite holographic spacetime within the TPST–DGQ framework. The paper reconstructs the internal logic of De Giuseppe’s argument, including the relation between ultraviolet divergence in Ryu–Takayanagi entanglement entropy, topological multiplicity, and the proposed Topological Emergence Identity. It then confronts this framework with the modal axioms, phenomenic structure, inductive effects, cosmogenic theorem, and cosmological eras of the Theory of Objectivity. The analysis argues that De Giuseppe’s proposal is highly original and structurally relevant, especially in its treatment of information, topological regulation, and emergent geometry. At the same time, it maintains that, under the modal discipline of TO, worldline non-injectivity should be understood not as an ultimate ontological foundation, but as a derived phenomenological mechanism of geometric stabilization within an already constituted cosmic regime. By placing contemporary holographic physics in critical dialogue with the Theory of Objectivity, the article seeks to clarify the distinction between mathematical consistency, phenomenological emergence, and modal foundation. It concludes that De Giuseppe’s model is best interpreted as a valuable partial theory of spacetime emergence, while TO preserves its claim to deeper cosmogenic and ontological priority. Keywords Theory of Objectivity; worldline non-injectivity; holographic spacetime; entanglement entropy; Ryu–Takayanagi formula; TPST–DGQ framework; modal ontology; spacetime emergence; topological regulation; phenomenic elements; inductive effects; cosmology; quantum information; AdS/CFT; critical–propositional analysis