An Alternative Bulk–Surface Field Model for Recursive Structure Formation, Bulk–Surface Coupling and Sequential Activation of Four Local Modes

This technical preprint presents a candidate bulk–surface field architecture for recursive local structure formation within the Harmonic Scale Framework (HSF). The selected realization consists of a complex CCE field in a compact bulk domain, a CCE surface realization on its closed spheroidal boundary, and four complex local modes representing active, coupling, collective, and locally stabilized roles. The model contains one permanent bidirectional interaction between CCE and the fundamental K1 mode. No direct CCE–K2, CCE–K3, or CCE–K4 interaction is introduced. Higher local modes are formed sequentially through neighboring amplitude-matching and phase-locking terms. The paper provides an explicit variational action, strong and weak bulk–surface field equations, a shared generator and energy-ownership rule, Cartesian null-sector curvatures, sequential formation thresholds, and a closed homogeneous periodic CCE–K1 relative equilibrium. It also derives reduced rotating-sector amplitude and phase curvatures, a dimensionless admissible parameter region, canonical nondimensionalization, parameter-gauge rules, structural-identifiability limits, and an inverse CCE–geometry formulation. The homogeneous solution and normalized parameter example demonstrate internal mathematical consistency only. They do not constitute a complete orbital, spatial, or nonlinear stability proof and are not an empirical calibration of CCE. Nonuniform bulk–surface solutions, the complete coupled spectrum, an SI calibration, a physical mapping from the ordering parameter to measured time, empirical CCE evidence, electron structure, gravitation, and a complete global K1–K8 field theory remain open. This work is a mathematical candidate architecture. It is not peer reviewed. The work presents a mathematical candidate architecture. The symbolic and normalized numerical results concern internal consistency only and do not constitute empirical validation of CCE or of HSF as a physical theory.