scalar_gap_normalization_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

Verify a classical scalar gap, its complete response, and fixed-norm counting.

The global scalar kernel is specified, not derived from the IDWT master law.
All complex modes belong to one field; no quantum vacuum is assumed.

Research context

Scalar gap with canonical normalization
A specified global scalar interaction admits a self-consistent gap and an exact collective response frequency, while canonical normalization determines whether a cumulative mode count enhances either quantity.
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.