smooth_current_projection_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

Exact current weights of a smooth coherent scalar projection.

The product calculation and partial-current calculation are independent.
This verifies the projection algebra and its canonical normalization; it
does not derive the different shell weights of the inverse mass action.

Research context

Current weights of the coherent scalar projection
Exact symmetric-index contractions identify the current weights of the smooth scalar kernel, while harmonic reconstruction and the canonical kinetic norm constrain routes to the simplex interaction.

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