TITLE:
Space Quantization in Hybrid Minkowski-Kähler Geometry via Idempotent Ramanujan Algebra: A Radon-Nikodym Energy Measure Approach to de Broglie Wavelengths, Dark Matter, and Dark Energy
AUTHORS:
Gruia Constantinescu
KEYWORDS:
Intrinsic Theory of Energy (ITE), Topological Mass, Radon-Nikodym Measure, Minkowski-Kähler Manifold, Electromagnetic Mass Dilemma, Vacuum Energy, Cosmological Constant
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.10,
October
12,
2026
ABSTRACT: Background: In quantum mechanics and general relativity, mass is treated as intrinsic or empirical, while electrodynamics faces divergence problems, including point-charge self-energy and the 4/3 electromagnetic mass dilemma. This paper introduces an idempotent Ramanujan algebraic representation of space, in which spatial structure is quantized through discrete algebraic units before being embedded in the hybrid Minkowski-Kähler manifold framework of the Intrinsic Theory of Energy (ITE). Within this setting, inertial mass is derived geometrically rather than postulated. Methods: Starting from the idempotent Ramanujan algebra, we construct a quantized spatial lattice of hybrid geometric nodes and use it to define an energetic measure of Radon-Nikodym type. We isolate free gauge-field radiant energy from total localized energy, map wave-function curvature to the Ricci scalar of the hybrid geometry and define an energy deficit measure. This positive Radon measure expresses mass as the Radon-Nikodym derivative of total phase energy with respect to captive energy. Results: The Ramanujan-idempotent quantization provides the discrete spatial substrate on which the Radon-Nikodym energy measure is defined and from which the de Broglie wavelength relation is recovered as a consequence of energy-phase structuring. The obtained generalized mass formula resolves the 4/3 electromagnetic mass anomaly through metric trace contractions over the hybrid Minkowski-Kähler manifold, identifying Poincaré stresses [1] with the structural phase projection operator. The framework recovers the classical limit, proves stability for single-pixel topological nodes such as the electron, yields the proton-to-electron mass ratio via composite Kähler coupling, and removes the cosmological constant discrepancy by showing that unperturbed vacuum has zero gravitational rest mass. Conclusions: Mass appears as a topologically bounded geometric mediator between quantum action, quantized spatial algebra, and spacetime curvature. On a hybrid Minkowski-Kähler manifold structured by idempotent Ramanujan algebra, matter is geometry, inertia is resistance to phase deformation under velocity changes, and dark-sector effects emerge from the same Radon-Nikodym energetic measure.