localized_harmonic_response.py

IDWT's physical premise is one infinite-dimensional manifold with all sectors nested as submanifolds. Particle depth counts macroscopic spatial dimensions; matrix and field-component counts in a calculation add no physical dimensions.

Calculation record

Higher angular harmonic-gradient response of the same localized action.

The integer ell labels ordinary spatial spherical harmonics, not the
occupied coefficient grade N or the physical depth d. The complete
ordinary/conjugate spinor and partner variations within each stated
closed angular family are retained.

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.

Interpret numerical checks within the assumptions and limitations documented in these notes.