coherent_mode_algebra.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

Finite symmetric-mode products and exact coherent contact coefficients.

The projective mode space is auxiliary. No particle action, physical spatial
geometry, or observed coupling is inferred from these coefficient operations.
Large physical bands use the scalar formulas rather than dense matrices.

Research context

Coherent quartic variation
A smooth quartic action has exactly coherent extrema, an explicit complete mode Hessian and finite-mode orbital stability, with the smooth-contact frequency multiplier.
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.