LORENTZ TRANSFORMATIONS BEYOND INJECTIVITY: the Ziegelstein thought experiment, multi-sheet spacetime structure, and its critical–propositional confrontation with the Theory of Objectivity

This article presents a critical–propositional examination of Alex De Giuseppe’s 2026 preprint Lorentz Transformations beyond Injectivity: The Ziegelstein Gedankenexperiment and the Emergence of Multi-Sheet Spacetime: From the Bricks Paradox to Multi-Sheet Spacetime Structure, in dialogue with the Theory of Objectivity (TO). Written by Vidamor Cabannas and Denivaldo Silva, the study investigates the hypothesis that standard Lorentz transformations rely on an implicit assumption of injectivity and that, beyond a critical threshold, they should be extended into a multi-sheet spacetime framework with topological phase offsets and multiple coordinated appearances of the same physical entity. The article argues that De Giuseppe’s proposal has genuine heuristic and philosophical value, especially in exposing silent assumptions within the standard relativistic formalism and in reopening the question of physical identity beyond instantaneous spatial localization. At the same time, the study maintains that, under the modal discipline of the Theory of Objectivity, the multi-sheet spacetime model cannot be accepted as an ultimate ontological foundation. Instead, it is reinterpreted as a late phenomenic formalization of deeper processes involving boundary, composition, observational convergence, and informational transcendence. The paper develops this confrontation through the Seven Absolute Truths of the Theory of Objectivity, the phenomenic elements, the Inductor Effects, the cosmogonic theorem, and the cosmological Eras of TO. In doing so, it preserves the regional explanatory value of De Giuseppe’s formalism while subordinating it to a broader modal ontology. The result is not a rejection of the multi-sheet hypothesis, but a disciplined incorporation of it as a derived and phenomenologically significant structure. This analytical study also records that the text was produced with the analytical support of ChatGPT. Keywords Lorentz transformations; non-injectivity; multi-sheet spacetime; Theory of Objectivity; modal ontology; phenomenic elements; Inductor Effects; cosmology; holography; ontological identity; relativistic kinematics; philosophy of physics; Alex De Giuseppe; critical–propositional analysis; ChatGPT-assisted analysis.