We present the parameter-taxonomy paper of the FCLET polar shell-scattering program, establishing a complete classification of how independent parameters deform the resonance structure governing gravitational–scalar conversion. Building on the corrected two-channel framework and on the avoided-crossing mechanism identified previously, we demonstrate that FCLET shell transparency is not controlled by a single effective coupling strength. Instead, it is governed by a structured resonance morphology shaped by six orthogonal parameter directions. The shell amplitude acts as a spectral driver, shifting branch frequencies and determining the location of transparency dips. The scalar mass acts as a freeze-out control, suppressing scalar propagation kinematically. The quartic kinetic parameter is amplitude-only, rescaling coupling strength without altering the spectral architecture. The shell radius is spectral-geometric, remapping resonance frequencies and dip positions. The multipole index defines a universal spectral scale, with the avoided-crossing gap scaling approximately with . Finally, the shell width acts as a sharpness modulator, reshaping dip depth, narrowness, and gap magnitude. These parameters do not compete redundantly. They act in approximately orthogonal directions in the space of resonance morphology. FCLET shell transparency is therefore a resonance-geometry problem rather than a single-parameter transmission effect. This work provides the first complete parameter taxonomy of FCLET shell scattering and establishes the structural foundation for future phenomenological and observational applications.
Ali Caner Yücel (Tue,) studied this question.