coherent_kernel_consistency_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

Coherent contact across bands, finite source widths and effective reductions.

Tests specify the band identification and distinguish a fixed bare form from
its frequency-dependent Schur reduction. No physical kernel is inferred.

Research context

Consistent band contacts
A fixed bare kernel must have compatible cumulative compressions, while coherent projective contact changes under the standard band inclusion and effective kernels obey a different Schur consistency law.
Finite ray resolution
A normalized coherent symbol of specified finite width has an exact full Toeplitz spectrum and a controlled point-contact error, with distinct fixed-width and fixed-band limits.
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.