Emergent Gravity, the Cosmological Constant, and Peccei–Quinn Symmetry under Ontological Discipline A critical–propositional reading of Petre Toader's IFD v5 in light of the Theory of Objectivity

This article develops an expanded critical–propositional analysis of Petre Toader’s Informational Foundation of Dynamics (IFD) v5, focusing on its central claims that (i) spacetime curvature can be identified with the Berry curvature of a position-dependent informational projector , (ii) the stability operator yields the gravitational effective field theory (Einstein–Hilbert term, cubic self-interaction, and quadratic curvature corrections), (iii) a normalization constraint removes the dilaton while preserving a physical zero mode interpreted as Peccei–Quinn symmetry, predicting an ultra-light axion, and (iv) the cosmological constant emerges as iterative misalignment across a -hierarchy from the Planck scale to the Hubble scale, avoiding ad hoc fine-tuning. The study confronts these theses with the modal-axiomatic discipline of the Theory of Objectivity (TO) (Cabannas & Silva 2016, 2018, 2020, 2025, 2026), treating TO not as a substitute for contemporary physics but as a necessary logical, ontological, and scientific foundation for any coherent model of a possible universe. Particular emphasis is placed on compatibilities and tensions with TO’s seven axioms (modal necessity), TO’s recent framework of Gödelian discipline and operational bridges, and TO’s phenomenic vocabulary (e.g., relational observability, boundaries, convergence zones). A key interpretive move is the TO-oriented identification of the “transcendent substance” (Axiom 7) with knowledge/information produced in atomic relations, considered equivalent to atomic radiations. Under this premise, the article proposes a translation of IFD’s “informational geometry” into a TO-compatible reading in which emergent gravity and the cosmological constant become late geometric manifestations of deeper relational–informational–radiative organization, while also highlighting remaining ontological gaps—especially the need to ground the IFD formal primitives in Nothingness as a primitive mathematical essence and to clarify the role of infinity as the logical non-element (Axioms 1 and 3). Beyond conceptual assessment, the article situates IFD v5 within broader debates on emergent spacetime, quantum gravity, vacuum structure, and cosmological testability, offering a structured TO-style appendix that organizes conceptual translations and research directions for future dialogue articles in the Theory of Objectivity Community. KeywordsTheory of Objectivity; modal ontology; ontological discipline; emergent gravity; informational geometry; Berry curvature; Riemann curvature; cosmological constant problem; Peccei–Quinn symmetry; axion; vacuum structure; effective field theory of gravity; inflation; Gödelian discipline; operational bridges; relational observability; convergence zones; atomic radiation; information flux; Petre Toader; IFD v5; Zenodo.