Calculation record
Spatial response in complete constant-Clifford angular multiplets.
For a Hermitian Clifford k-form T, the span of T, alpha_r T, T alpha_r,
and alpha_r T alpha_r is closed under the actual radial background Hessian.
It includes nonradial polarization modes and translations. Higher spherical
harmonic multiplets remain outside this finite angular test.
Research context
- Higher angular response of the localized current field
Homogeneous closed and coclosed polynomial forms give complete angular blocks for the even-depth matrix field; independent Cartesian checks and expanded electron and muon scans retain the distinction between angular classification and full spatial stability.
- Response of localized simplex-frequency fields
Solved localized branches have identical finite lower-grade probe energies and forces at common profile, while complete current Hessians and bounded spatial spectra distinguish that coupling identity from stability.
Interpret numerical checks within the assumptions and limitations documented in these notes.