scaled_gap_core.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

Common-gap fixed points with a dimensionless binding coefficient.

The exponent a=1/d is the one that makes g dimensionless with canonical
Dirac field scaling in d+1 spacetime dimensions. This optional scaling
principle does not derive the interaction or identify amplitude as mass.

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.