shape-frequency-mobility-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

Diagnostic implementation referenced by the research record.

Research context

Shape-Frequency Mobility for Classical Spatial Patterns
The original centroid-capped Gaussian action has a positive restricted phase response but fails the uniform-phase Gaussian traveling equation. Changed phase actions give exact positive Gaussian travel and a conditional frequency-following mobility theorem; the actual Gaussian satisfies the latter action against all compact smooth field variations. Global Cauchy theory does not transfer.

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