smoothed-count-pattern-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 rational checks of the changed Gaussian-smoothed count action.

Research context

A Smoothed Count Action with Global Finite-Energy Histories
A Gaussian-smoothed classical density action preserves 960 supplied count-clock branches, admits nodal finite-energy fields, and has a continuous L2 source and global norm-conserving weak and mild histories. Its complete Gaussian density Hessian is nonnegative in every spatial degree. Counts and sector units remain inputs, general uniqueness is open, energy is conserved, and its Galilean inertia does not follow the count frequency.

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