local_scalar_response_rank_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

Pointwise scalar-source rank, exact response bounds and kinetic activation.

These are conditional properties of the written local scalar Dirac term.
Full source rank is not the rank of a projected particle vertex. The plane
activation control is unbound and contains both signs of free kinetic energy.

Research context

Complete scalar response and null directions
The complete local scalar-source derivative is invertible at nonzero scalar density, while a scalar-null field retains one real response direction whose kinetic protection and projected channel meaning must be tested separately.
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.