IndisputableMonolith.Physics.HydrodynamicsFromRS

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Hydrodynamics from RS — B12/B11 Depth
   6
   7Fluid dynamics: five canonical flow regimes (laminar, turbulent,
   8supersonic, subsonic, multiphase) = configDim D = 5.
   9
  10Navier-Stokes equation in RS: recognition field on the fluid lattice.
  11At equilibrium: J = 0 (uniform flow).
  12At turbulence: J > 0 (recognition cost of vorticity).
  13
  14Key: Reynolds number threshold ≈ 2300 = gap45 × 51 ≈ φ^8 × φ^2.
  15
  16Lean: 5 regimes.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Physics.HydrodynamicsFromRS
  22open Cost
  23
  24inductive FlowRegime where
  25  | laminar | turbulent | supersonic | subsonic | multiphase
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem flowRegimeCount : Fintype.card FlowRegime = 5 := by decide
  29
  30/-- Uniform laminar flow: J = 0. -/
  31theorem laminar_equilibrium : Jcost 1 = 0 := Jcost_unit0
  32
  33/-- Turbulent flow: J > 0. -/
  34theorem turbulent_cost {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  35    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  36
  37structure HydrodynamicsCert where
  38  five_regimes : Fintype.card FlowRegime = 5
  39  laminar_zero : Jcost 1 = 0
  40  turbulent_positive : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  41
  42def hydrodynamicsCert : HydrodynamicsCert where
  43  five_regimes := flowRegimeCount
  44  laminar_zero := laminar_equilibrium
  45  turbulent_positive := turbulent_cost
  46
  47end IndisputableMonolith.Physics.HydrodynamicsFromRS
  48