Limiting Recoveries of Established Physical Laws from a Geometric Helical Field Framework

Abstract We present the second installment of the Geometric Helical Field Theory, focusing on the systematic recovery of established physical laws as limiting regimes of a single background-independent geometric framework. Building upon the fundamental helical field structure introduced in Paper I , we demonstrate how classical and relativistic descriptions emerge without being postulated a priori. An effective spectral energy density, constructed solely from the intrinsic geometry and topology of the helical field, is shown to generate a consistent geometric back-reaction. In appropriate weak-gradient and large-scale limits, this back-reaction reproduces Newtonian gravity, while its covariant extension yields correspondence with the Einstein field equations. The emergence of relativistic effects is traced to Lorentz-consistent geometric constraints rather than independent dynamical assumptions. Electromagnetic radiation and Maxwellian behavior arise as limiting cases associated with the local relaxation of helical constraints, whereas Planckian spectral relations appear as effective quantities in the asymptotic spectral regime. Throughout the analysis, no external forces, background spacetime, or fundamental constants are assumed; all physical constants enter as emergent, scale-dependent parameters. The framework is shown to be internally consistent, mathematically well-defined, and explicitly compatible with known experimental limits. At the same time, it remains open to systematic extensions beyond the classical and relativistic domains, providing a controlled geometric setting for future investigations into quantum and cosmological regimes.