TEMPORAL NON-INJECTIVITY AND MULTI-SHEET SPACETIME: a critical–propositional analysis 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 Alex De Giuseppe’s paper Temporal Non-Injectivity and Multi-Sheet Spacetime: A Sheaf-Theoretic Approach to Closed Timelike Curves and UV Regularisation (2026), published on Zenodo under DOI https://doi.org/10.5281/zenodo.20551209. The study examines De Giuseppe’s proposal in confrontation with the axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras of the Theory of Objectivity, developed by Vidamor Cabannas and Denivaldo Silva. The analysis argues that De Giuseppe’s model of temporal non-injectivity, multi-sheet spacetime, sheaf-theoretic time, monodromy, deck transformations, Weyl algebra, and topological averaging offers a highly productive formal dialogue with the Theory of Objectivity. Special attention is given to the ontological role of boundary, the preservation of identity across multiple temporal sheets, the interpretation of monodromy as topological memory, and the possible reading of informational transcendence as knowledge or information produced in atomic relations and equivalent to atomic radiations within the conceptual framework of TO. The article also identifies important points of tension: De Giuseppe’s framework remains primarily kinematic, topological, and mathematical, while the Theory of Objectivity is presented as a modal, ontological, and cosmogonic framework grounded in seven necessary axioms. Therefore, the analyzed paper is interpreted not as a direct empirical confirmation of TO, but as a strong formal bridge for dialogue with contemporary theoretical physics, especially in discussions concerning time, singularities, ultraviolet regularisation, causality, Taub–NUT spacetime, and the structural foundations of physical reality. This analytical text received analytical support from ChatGPT. Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Alex De Giuseppe; temporal non-injectivity; multi-sheet spacetime; sheaf theory; monodromy; Taub–NUT spacetime; ultraviolet regularisation; Weyl algebra; topological averaging; Inducer Effects; phenomenic elements; modal ontology; cosmogonic theorem; cosmological Eras; informational transcendence; atomic radiation.