entropy-difference-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

Standalone exact finite checks for the entropy-difference pattern action.

Run: python3 -B entropy-difference-pattern-checks.py
Requires Python 3 and SymPy. Writes a dated JSON report beside this script.
Finite identities support the analytical arguments; they are not a PDE proof.
The scalar field occupies ordinary R10; widths do not imply absent dimensions.

Research context

Entropy-Difference Field Action with Exact Localized Patterns and Global Evolution
A signed Gaussian entropy-difference action has exact moving two-width Gaussian patterns, global finite-energy evolution and Gaussian-family persistence. Its complete Hermite spectrum has growing non-Gaussian modes, and finitely many filters of the same type cannot stabilize every mixed-width branch. The common support clock does not derive the particle mass family.

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