Arithmetic Cosmology: The Topological Origin of Vacuum Energy and the Stability of the Prime Manifold via ROA

As the final installment of the Seonggil Matrix series, this paper establishes a unified cosmological model derived from the structural imperatives of arithmetic. We propose that the Cosmological Constant (Λ) is not an arbitrary physical parameter but a topological pressure, Λarith, emergent from the non-commutative torsion of the prime manifold. By synthesizing our previous findings on arithmetic thermodynamics and motivic cohomology, we derive a direct relationship between Λarith, Planck’s constant (h), and the Golden Ratio(ϕ). We prove that the accelerated expansion of the universe is a structural necessity tomaintain the non-resonant phase locking of the vacuum, effectively preventing the arithmetic singularity of perfect symmetry (I(n) = 2). This framework concludes the Seonggil Matrix Theory, positioning the universe as a self-tuning arithmetic engine.