The Hyperspheric Wave Front (HWF): Matter and Radiation as Open and Confined Modes of the Complex Continuum

A physical extension of the Hyperspheric Wave Front (HWF) framework is presented to investigate the possibility of describing matter and radiation as two dynamical regimes of the same physical structure. The model is formulated on the complex space C₇ and introduces the Complex Continuum (CC) as a continuous physical field defined over this geometry, of which the Hyperspheric Wave Front constitutes a transverse excitation. Radiation is interpreted as an open propagative regime, whereas matter is investigated as a localized and self-confined internal configuration. Starting from the HWF Fundamental Equation, an effective reduction to the internal sector is developed. Under a local approximation, a quasi-stationary ansatz, and an effective nonlinear self-interaction, the reduced dynamics is found to be compatible with spatially localized, finite-energy profiles. The confined energy then provides a basis for interpreting mass as the energy of a persistent internal organization. A phenomenological characterization of the CC is also explored, and structural regularities and coincidences with part of the known spectrum are identified, while explicitly distinguishing among derived results, effective hypotheses, calibrated quantities, and interpretations. The model does not yet derive from first principles the fundamental self-interaction of the CC, the particle spectrum, or the full stability of the confined modes. The main result is the establishment of a common physical architecture in which matter and radiation can be investigated as different dynamical organizations of the same HWF excitation, while leaving their quantitative determination and independent tests as open problems.