Calculation record
Direct radial ODE matching for candidate angular growing modes.
A growing localized mode must be regular at the origin and lie in the
exponentially decaying far-field subspace. Finite outer-radius matching is
an independent control, not an exhaustive spectral or nonlinear theorem.
Research context
- The spatial response of a shape-preserving mass core
A positive scalar/vector shape penalty preserves the mass-frequency and inertia branch while changing the complete local response; spatial angular matching distinguishes finite-basis candidates from localized growing modes.
Interpret numerical checks within the assumptions and limitations documented in these notes.