Wave-Particle Duality as Virtual-Real Domain Manifestation: Resolving Complementarity Through Dual Regulator Framework

This paper presents a finite, regulator-based resolution of wave–particle duality, showing that quantum duality is not a fundamental paradox but a natural consequence of domain separation. Within the Dual Regulator Framework, wave behavior is shown to arise exclusively in the virtual domain (momentum space, off-shell propagation), regulated by the finite invariant Λφ=ln⁡(φ2),\Lambda_\varphi = \ln(\varphi^2),Λφ=ln(φ2), while particle behavior arises exclusively in the real domain (position space, on-shell detection), regulated by the Resolution Gap RG=ln⁡(φ)/ln⁡(π).\mathrm{RG} = \ln(\varphi)/\ln(\pi).RG=ln(φ)/ln(π). The double-slit experiment is reinterpreted as a virtual-domain interference process followed by a real-domain localization event. Which-path detection is shown to force a premature virtual-to-real transition, preventing interference from forming. Partial which-path information produces a quantitative reduction in visibility governed by a finite exponential law. The framework yields explicit, testable predictions with zero adjustable parameters, including: a φ-harmonic correction to interference fringe spacing, a sharp detector-coupling threshold for which-path information, an exact functional form for visibility–distinguishability relations, and scale-dependent corrections for matter-wave interferometry (electrons, neutrons, molecules). All results derive solely from the Trinity constants {π, φ, e}. Complementarity is shown to be a consequence of domain incompatibility, not a primitive principle. Wave–particle duality dissolves into a physically interpretable, observer-independent mechanism. This paper forms Paper II in a planned sequence addressing foundational inconsistencies in quantum field theory, following the finite resolution of the measurement problem.