This paper demonstrates that quantization arises naturally in NUVO space from the geometric coherence of the scalar fieldλ,without invoking probabilistic or wave—mechanical postulates.By enforcing closure of the sca...This paper demonstrates that quantization arises naturally in NUVO space from the geometric coherence of the scalar fieldλ,without invoking probabilistic or wave—mechanical postulates.By enforcing closure of the scalar—weighted arc element on the conformal manifold(M,g)with g=λ^(2)η,discrete action levels are obtained.The coherence condition leads to a universal action constant,empirically identified withhwhen calibrated to the ground—state energy of hydrogen.This result establishes quantization as a geometric property of NUVO space itself,forming the bridge between scalar conformal geometry and microscopic physical structure.展开更多
We develop the analytic,geometric,and variational framework on NUVO space,the conformally flat manifold(M,g)with g=λ^(2)η introduced in Part I.Weighted divergence and Stokes theorems,curvature identities,and the Lap...We develop the analytic,geometric,and variational framework on NUVO space,the conformally flat manifold(M,g)with g=λ^(2)η introduced in Part I.Weighted divergence and Stokes theorems,curvature identities,and the Laplace-Beltrami operator are derived in full detail.We construct the variational principles governing geodesic motion and scalar currents and prove the existence and regularity of solutions to representative nonlinear scalar field equations.Together with Part I,this paper provides the mathematical foundation required for subsequent applications to gravitation and field dynamics.展开更多
We construct the differential-geometric foundation of NUVO space as a conformally flat manifold(M,g)endowed with a scalar unit constraint.Starting from a flat background formηand scalarλ>0,we derive the associate...We construct the differential-geometric foundation of NUVO space as a conformally flat manifold(M,g)endowed with a scalar unit constraint.Starting from a flat background formηand scalarλ>0,we derive the associated frame-bundle reduction,induced metric g=λ^(2)η,and Levi-Civita connection.Existence,uniqueness,and regularity of the induced connection are proved,defining the canonical calculus objects required for subsequent curvature and variational analyses.展开更多
文摘This paper demonstrates that quantization arises naturally in NUVO space from the geometric coherence of the scalar fieldλ,without invoking probabilistic or wave—mechanical postulates.By enforcing closure of the scalar—weighted arc element on the conformal manifold(M,g)with g=λ^(2)η,discrete action levels are obtained.The coherence condition leads to a universal action constant,empirically identified withhwhen calibrated to the ground—state energy of hydrogen.This result establishes quantization as a geometric property of NUVO space itself,forming the bridge between scalar conformal geometry and microscopic physical structure.
文摘We develop the analytic,geometric,and variational framework on NUVO space,the conformally flat manifold(M,g)with g=λ^(2)η introduced in Part I.Weighted divergence and Stokes theorems,curvature identities,and the Laplace-Beltrami operator are derived in full detail.We construct the variational principles governing geodesic motion and scalar currents and prove the existence and regularity of solutions to representative nonlinear scalar field equations.Together with Part I,this paper provides the mathematical foundation required for subsequent applications to gravitation and field dynamics.
文摘We construct the differential-geometric foundation of NUVO space as a conformally flat manifold(M,g)endowed with a scalar unit constraint.Starting from a flat background formηand scalarλ>0,we derive the associated frame-bundle reduction,induced metric g=λ^(2)η,and Levi-Civita connection.Existence,uniqueness,and regularity of the induced connection are proved,defining the canonical calculus objects required for subsequent curvature and variational analyses.
