inverse_scalar_law_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

Reconstruct a local scalar law from complete stationary spatial fields.

The inverse formula keeps complex field components and tests a common law.
Pure Jacobi pairs are an explicit ansatz; dressed fields remain available.

Research context

Reconstructing a scalar interaction from spatial particle fields
Complete spatial fields determine a scalar interaction only when their full residual is scalar and equal-current points require the same law; unchanged Jacobi pairs cannot share the assigned simplex frequencies through such a law, while nonlinear dressed controls reconstruct both the common action and its coupling derivative.
Diagnostic catalog
Reproduction commands and scope descriptions for every local finite diagnostic and helper.

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