High-contrast homogenization: Provider.Response.CutoffCoefficient

Imported from the Apache-2.0 HighContrastHomogenization development at commit 7a13dbcd8d6609264a713373f5c69ceeac870472.

The dimensional cutoff coefficient

The first adapted-coordinate derivative of the pre-Young cutoff is bounded by C_d 3^{-t}. Multiplication by the scale-s cell diameter therefore leaves the dimensional coefficient C_d and the scale-gap factor 3^{-H}, where H = t - s.

theorem HCPolySupport.HighContrast.Response.cutoff_energy_coefficient {Cd J : ℝ} {s t H : ℤ} (hH : H = t - s) : Cd * 3 ^ s * (3 ^ (-t) * J) = Cd * 3 ^ (-H) * J

The dimensional derivative bound contributes C_d 3^{-H} to the cutoff-energy term when H = t - s.