-- M001: Thermodynamic Stress Kernel Module
-- Source: burgers_heat_diffusion (3-Mathematical-Models)
-- Kernel Function: ThermalZoneManager
--
-- Models CPU/memory thermal zones as 1D Burgers equation states.
-- Thermal stress = velocity field u(x,t) where x=zone index, t=time.
-- Viscosity ν = thermal conductivity, shock waves = hot spots.
-- Truth Seal: [ SSS-ENE-THERMAL-2026-05-03 ]

module M001_ThermodynamicStress where

import BaseTypes
import Semantics.Q16_16 (Q16_16, add, sub, mul, div, ofNat, zero)

structure ThermalZone where
  id            : ZoneID
  position      : Q16_16          -- Spatial coordinate in thermal manifold
  temperature   : Q16_16          -- Current temperature (u)
  conductivity  : Q16_16          -- Thermal conductivity (ν)
  capacity      : Q16_16          -- Heat capacity
  powerDissipation : Q16_16       -- Power input (forcing term)
  neighbors     : Array ZoneID    -- Adjacent zones (for Laplacian)
  
def initThermalState (zones : Array ThermalZone) : ThermalState :=
  { zones := zones
  , dt := Q16_16.ofNat 1          -- 1 second timestep
  , dx := Q16_16.ofNat 1          -- 1 zone spacing
  , t := Q16_16.zero
  }

-- Burgers RHS: du/dt = ν·d²u/dx² - u·du/dx + forcing
-- Discretized with central differences

def burgersRHS (state : ThermalState) (idx : Nat) : Q16_16 :=
  let zone := state.zones[idx]
  let ν := zone.conductivity
  let u := zone.temperature
  
  -- Laplacian d²u/dx² = (u[i-1] - 2u[i] + u[i+1]) / dx²
  let left := state.zones[idx-1].temperature
  let right := state.zones[idx+1].temperature
  let laplacian := div (sub (add left right) (mul (Q16_16.ofNat 2) u)) (mul state.dx state.dx)
  
  -- Advection u·du/dx = u·(u[i+1] - u[i-1]) / 2dx
  let advection := mul u (div (sub right left) (mul (Q16_16.ofNat 2) state.dx))
  
  -- Forcing = power dissipation / capacity
  let forcing := div zone.powerDissipation zone.capacity
  
  -- RHS = ν·laplacian - advection + forcing
  add (sub (mul ν laplacian) advection) forcing

def thermalStep (state : ThermalState) : ThermalState :=
  let newZones := state.zones.map (\zone idx =>
    let rhs := burgersRHS state idx
    { zone with temperature := add zone.temperature (mul rhs state.dt) }
  )
  { state with zones := newZones, t := add state.t state.dt }

-- Stress metric: max |du/dx| (thermal gradient shock indicator)

def thermalStressMetric (state : ThermalState) : Q16_16 :=
  let gradients := state.zones.map (\zone idx =>
    if idx < state.zones.size - 1 then
      let right := state.zones[idx+1].temperature
      abs (sub right zone.temperature)
    else
      Q16_16.zero
  )
  gradients.maximum

-- Kernel syscall interface: get thermal stress recommendation

def syscallThermalStress (zoneId : ZoneID) : IO ThermalReport := do
  let zone ← findZone zoneId
  let state ← readThermalState
  let stress := thermalStressMetric state
  let recommendation :=
    if stress > THERMAL_CRITICAL then
      .EmergencyThrottle
    else if stress > THERMAL_WARNING then
      .ReduceClock
    else
      .Normal
  
  return {
    zone := zone
    temperature := zone.temperature
    stressLevel := stress
    action := recommendation
    timestamp := now ()
  }

end M001_ThermodynamicStress