scaled_gap_core_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

Depth-dependent common-gap cores, exact scale law and full Dirac checks.

The dimensionless binding principle is an inverse premise. The frequency
unit, canonical one-particle norm and physical coupling channels are not
forward-derived by these checks.

Research context

Dimensionless binding and depth-dependent cavity scales
A dimensionless binding principle selects the core exponent and yields localized depth-five, six and ten profiles with explicit common-size factors, while the gap-to-frequency relation and physical normalization remain inverse conditions.

Interpret numerical checks within the assumptions and limitations documented in these notes.