biased_source_compatibility_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

Exact finite-harmonic compatibility checks for one response per depth.

The source vectors are algebraic controls, not physical measurements. The
calculation asks whether one depth-wide bias can make every maintained mode
orthogonal to its eliminated positive response on an explicit finite harmonic
control space. The infinite completion is checked by the companion script.

Research context

Finite biased support and the mode-selection boundary
One positive response bias can satisfy the field-orthogonality equations for a finite selected set at each depth, but the same bias fails the next unselected mode and therefore requires a derived mode-selection law.
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.