dimensional_necessity_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

Dimension-discrimination checks with explicit counterexamples.

No particle is reassigned. Tests compare the same diagnostic equations on
counterfactual ambient spaces and prove finite algebraic identities.

Research context

Dimensional necessity from response
A fixed-preparation unobserved-response rank theorem gives a conditional six-dimensional lower bound, while exact five-dimensional dynamics and averaging counterexamples identify what the existing constructions do not require.

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