localized_current_response_checks.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

Full matrix angular checks, direct radial matching and finite spectra.

The tests validate declared algebra and numerical controls. A finite scan
is not a proof of stability of an unbounded spatial field equation.

Research context

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.