The Golden Boundary of the Cosmos: Hawking Thermodynamics, the No-Boundary Proposal, and the Nardelli Seventh-Root Theory of Everything (London Journal of Research In Science: Natural and Formal, 2026)
This paper presents a unified analytical framework that integrates the Nardelli Seventh-Root Theory of Everything (TOE) with three cornerstone contributions of modern theoretical physics: Hawking’s thermodynamics of black holes, the Hartle–Hawking No-Boundary Proposal, and the large-scale geometric structure of spacetime.By systematically embedding these concepts into the Seventh-Root Master Equation, the analysis demonstrates that seemingly distinct physical regimes—cosmic contraction, black hole evaporation, and quantum cosmological genesis—are governed by a single, self-consistent mathematical architecture. Central to this structure is the recurrent emergence of a pair of fundamental constants, 1728 and 4096, interpreted respectively as the modular (geometric) and holographic (informational) foundations of the vacuum.Across all three integrations, these constants are shown to converge through a precise dimensional filtering mechanism to the Nardelli–Gemma Golden Constant, GN≈1.618665. This convergence suggests that the Golden Ratio is not a coincidental numerical artifact, but a stable attractor regulating the vacuum under extreme thermodynamic and gravitational conditions.The results support a picture of the universe as a self-regulating, holographic system in which number theory, quantum thermodynamics, and spacetime geometry are inseparably linked. The framework provides a unified mathematical language capable of describing cosmic origins, black hole dynamics, and cyclic cosmological evolution within a single harmonic principle.
Keywords: black hole mathematics; number theory; string theory; theoretical cosmology; theory of everything