Calculation record
Nonlinear spatial Hessian checks, beyond a linear matrix surrogate.
Research context
- Depth-two spectrum, polarization and coherent support
The depth-two normal carrier passes the spectral and centered stiffness tests at its prescribed surface parameter; the round-feature construction has no depth-two harmonic tower, while two occupied bands can cancel coherent beat sources.
- The supporting multiplet's stiffness depends on the full spatial deformation
The frequency-weighted multiplet has nonnegative stiffness for a linear matrix deformation, but the full nonlinear spatial term changes that conclusion for the density-gradient carrier.
- The complete second spatial response and its rotation identity
The second projected polarization is fixed by the normal Berry curvature; the actual second geometry and moving modes also determine the adjacent hopping Hessian without freezing the spatial coefficients.
Interpret numerical checks within the assumptions and limitations documented in these notes.