Conformal Quantum Gravity and a Three‑Dimensional Network of Strings

Abstract

We present a self‑contained academic review and synthesis of two independent models that converge on a unified picture of quantum gravity and emergent spacetime. Model A (Prokhorov) derives quantum mechanics and string theory from first principles: classical oscillators coupled to a stochastic thermostat reproduce the Fock‑space structure of QFT, and ordered chains of such oscillators yield the Nambu–Goto action. Space emerges as a three‑dimensional network of bosonic strings whose topology is selected by the Principle of Maximal Stability (PMS). Model B (Hamada) constructs a perturbatively renormalizable quantum gravity in four dimensions from the Weyl‑tensor‑squared and Gauss–Bonnet action. The conformal anomaly generates a dynamical scale via dimensional transmutation; a phase transition condenses the conformal mode, producing the Einstein–Hilbert action, the Planck mass and an exponentially suppressed cosmological constant. We construct a detailed dictionary mapping the structures of the two models onto one another (thermostat ↔ conformal anomaly, triple junction ↔ CP² instanton, PMS ↔ self‑duality, network defects ↔ dark particles). A Lorentz‑violation theorem for a dynamical Z³ lattice is formalised and machine‑verified in Lean 4. The synthesis provides a coherent framework in which the discrete and continuum descriptions of quantum gravity are two complementary aspects of a single underlying reality.