Provider #
Ported from scottnarmstrong/Superdiffusion at 7f20476385d4af418f110303085ad0740c9eba46. Module imports, support namespace and local option directives adapted for Lean Pool.
The unconditional response estimate #
Source: ABK26, the J half of l.J.sensitivity.no.conditions.
Provider.ResponseUnconditional.Closure reduces the frozen target
Algsuperdiff.Frozen.Section24.responseJ_sensitivity_unconditional to a single
analytic input, the per-mesoscopic-cube conditional J-sensitivity at the
normalized loading p = (μσ₀)^{-1/2} e, q = (μσ₀)^{1/2} e.
Provider.ResponseUnconditional.CubeSensitivity proves exactly that input at a
general loading. This module instantiates the loading and assembles the
provider.
At the normalized loading
|p|² = (μσ₀)^{-1} , |p·q| = |e|² = 1 ,
which is precisely the pairing of the two K₁ groups of the frozen statement,
and at a cube of depth H below the unit cube
|R|² = 3^{-2H}, the damping factor of the frozen statement.
The value budget is Provider.ResponseUnconditional.valueBudget, whose depth-H
descendant average over the unit cube is exactly ‖h‖²_{L²(□₀)}.
The normalized loading #
The per-mesoscopic-cube input #
The per-mesoscopic-cube conditional J-sensitivity at the normalized
loading, in exactly the shape consumed by
responseJ_sensitivity_unconditional_of_mesoscale_cube_sensitivity.
The provider #
Unconditional four-term sensitivity estimate for the response functional.
This is the provider form of the frozen target
Algsuperdiff.Frozen.Section24.responseJ_sensitivity_unconditional, with
exactly the frozen binders.