IndisputableMonolith.ILG.PressureForm

   1import Mathlib
   2
   3/-!
   4# ILG as Pressure Display (scaffold)
   5
   6Algebraic display equivalence: rewrite the ILG effective source term using a
   7pressure variable `p := ρ · w(k,a) · δ`, keeping the physics unchanged.
   8-/
   9
  10namespace IndisputableMonolith
  11namespace ILG
  12namespace PressureForm
  13
  14open scoped Real
  15
  16/- Global constants bundle (only `G` used here for display). -/
  17structure Phys where
  18  G : ℝ
  19  deriving Repr
  20
  21/- Generic kernel placeholder `W` (the ILG kernel `w(k,a)`). -/
  22abbrev Kernel := ℝ → ℝ → ℝ
  23
  24/- Effective source in Poisson/growth (ILG display): 4π G a^2 ρ w δ. -/
  25def effectiveSource (P : Phys) (W : Kernel) (k a ρ δ : ℝ) : ℝ :=
  26  4 * Real.pi * P.G * (a ^ 2) * ρ * (W k a) * δ
  27
  28/- Pressure display variable p := ρ · w · δ. -/
  29def pressure (W : Kernel) (k a ρ δ : ℝ) : ℝ := ρ * (W k a) * δ
  30
  31/- Effective source via pressure display: 4π G a^2 p. -/
  32def effectiveSource_pressure (P : Phys) (W : Kernel) (k a ρ δ : ℝ) : ℝ :=
  33  4 * Real.pi * P.G * (a ^ 2) * pressure W k a ρ δ
  34
  35/- Algebraic equivalence (display-only): identical right-hand sides. -/
  36theorem source_equiv (P : Phys) (W : Kernel) (k a ρ δ : ℝ) :
  37  effectiveSource P W k a ρ δ = effectiveSource_pressure P W k a ρ δ := rfl
  38
  39end PressureForm
  40end ILG
  41end IndisputableMonolith
  42