Quantum Information and the Deep Structure of the Gravitational Field: Spacetime Entanglement, the Microstructure of the Scalar Field N(x) and the Ultimate Cosmology

This third and concluding essay of the foundational trilogy on Informational Scalar-Tensor Gravity (ISTG) extends the framework toward the quantum regime and examines its possible foundational implications. The central hypothesis investigated is that the scalar informational field N(x) may admit a microscopic interpretation in terms of the quantum correlations and entanglement structure of the spacetime vacuum. Rather than assuming this identification as an established result, the essay formulates it as a possible bridge between the effective scalar-tensor description developed in the preceding essays and a more fundamental quantum-informational theory. The work examines the possible quantum origin of the informational field, the effective action and renormalization structure of the theory, black-hole information, strong-field configurations, the Page-curve problem, and the possible holographic interpretation of the scalar field. A preliminary computational model of black-hole evaporation is also presented as a phenomenological scaffold rather than as a derivation from a microscopic quantum theory. Particular attention is given to the distinction between the established effective structure of ISTG and its still conjectural ultraviolet and quantum interpretation. The proposed hierarchy from quantum degrees of freedom and entanglement structure to the effective field N(x), the coupling F(N), and spacetime geometry is therefore presented as a research programme requiring explicit microscopic derivation, semiclassical recovery, consistency tests, and observational or theoretical falsification. The essay does not claim to constitute a completed theory of quantum gravity. Its purpose is to formulate the mathematical structures, hypotheses, and open problems required for a possible quantum extension of Informational Scalar-Tensor Gravity.