slow_shape_pole_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

Signed slow poles of the full two-frequency scalar shape response.

The meromorphic response retains both Dirac signs and its canonical form.
A slow pole does not establish a stable particle or a weak total response.

Research context

Slow shape poles and their signed response
The two-frequency scalar shape response has poles whose frequency and residue decrease together, but their canonical sign and finite total response prevent identifying them from softness alone as stable weakly coupled particles.
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.