spectral_count_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

Check state counts, spatial projectors and response in declared analogues.

These are scalar oscillator and quasiperiodic lattice controls, not IDWT
particle solutions. No physical particle indices or masses are fitted.

Research context

Common cavity size and collective coupling
A common cavity radius and count-additive energy constrain the balancing terms of an inverse action, while its canonical probe response requires a separate count scaling that can be tested against actual spatial contacts.
Spectral counts in a responsive cavity
A gapped spatial band retains its cumulative count while its projector and coupling change; a reciprocal quasiperiodic phase gives a complete spatial response and nonlinear field evolution that test a low-frequency inertia reduction.
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.