ZV₂₃: The Ring of Rotational Integers - Unifying Arithmetic and Physics

This paper proposes a radical reinterpretation of number theory: integers are not abstract symbols but physical operators acting on a discrete 23-dimensional vacuum lattice (V₂₃). The ring ZV₂₃ of "rotational integers" is algebraically isomorphic to the Gaussian integers ℤ[i] but represents torsional rotations in structured spacetime. Under this framework:- Prime numbers correspond to elementary particles with masses m ∝ √p- Quadratic reciprocity becomes a quantum commutation relation - The Riemann ζ-function emerges as a spectral trace- Integer factorization reduces to quantum resonance measurement This work is programmatic in nature. Several key results are presented as conjectures requiring rigorous proof. We provide the conceptual framework and physical motivation; detailed mathematical development is ongoing. If even partially correct, this framework represents a fundamental unification of arithmetic, geometry, and quantum physics. All claims are falsifiable through high-energy physics experiments (mass spectrum predictions) and quantum computing implementations (factorization algorithm). The paper invites mathematical verification, experimental testing, and critical engagement from the number theory, quantum physics, and quantum computing communities.