IndisputableMonolith.ClassicalBridge.Fluids.Bridge

   1import Mathlib
   2import IndisputableMonolith.ClassicalBridge.Fluids.Discrete
   3import IndisputableMonolith.ClassicalBridge.Fluids.LNAL
   4import IndisputableMonolith.ClassicalBridge.Fluids.CPM
   5
   6namespace IndisputableMonolith
   7namespace ClassicalBridge
   8namespace Fluids
   9
  10/-!
  11# RS ↔ Navier–Stokes Bridge: specification
  12
  13This is an *interface* capturing what a complete RS-native NS proof needs:
  14
  151. A discrete NS approximation (`DiscreteModel`)
  162. An LNAL spatial semantics and an encoding/decoding
  173. A simulation statement relating (2) to (1)
  184. A CPM instantiation on the discrete state
  195. Uniform bounds + continuum limit + global regularity statements
  20
  21This file intentionally avoids “proving the world” up front. It defines the
  22objects we will later implement and prove.
  23-/
  24
  25/-- Bundle of RS↔NS bridge requirements (spec-level). -/
  26structure RSNSBridgeSpec where
  27  /- Parameters and discrete approximation -/
  28  params   : NSParams
  29  dt       : TimeStep
  30  discrete : DiscreteModel
  31
  32  /- LNAL side -/
  33  program   : IndisputableMonolith.LNAL.LProgram
  34  semantics : SpatialSemantics
  35  encode    : discrete.State → LNALField
  36  decode    : LNALField → discrete.State
  37
  38  /- Correctness statements (to be proved, or made explicit hypotheses) -/
  39  /-- LNAL simulates the discrete model (exactly or with a stated error model). -/
  40  simulates : Prop
  41
  42  /- CPM instantiation -/
  43  cpm : CPMBridge discrete.State
  44
  45  /- Analysis-layer outcomes -/
  46  /-- Uniform bounds needed to pass to the continuum (typically independent of truncation). -/
  47  uniformBounds : Prop
  48  /-- Discrete → continuum limit theorem in the chosen solution concept. -/
  49  continuumLimit : Prop
  50  /-- The final global regularity statement (the target theorem). -/
  51  globalRegularity : Prop
  52
  53/-- “Verified” just means all declared bridge properties hold. -/
  54@[simp] def RSNSBridgeSpec.verified (S : RSNSBridgeSpec) : Prop :=
  55  S.simulates ∧ S.uniformBounds ∧ S.continuumLimit ∧ S.globalRegularity
  56
  57end Fluids
  58end ClassicalBridge
  59end IndisputableMonolith
  60