/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Research Stack Team

FieldDamping.lean — Field Damping for Resonant Field Propagation

Defines field damping mechanisms for Resonant Field Propagation (RFP).
Damping prevents runaway oscillation and ensures stability.

Per AGENTS.md:
  - Q16_16 for scoring (§1.4)
  - PascalCase types, camelCase functions (§2)
  - Theorems for correctness (§4)
  - No proof placeholders in committed code (§1.6)
-/

import Mathlib.Data.Nat.Basic
import Mathlib.Data.List.Basic
import Mathlib.Data.Fin.Basic
import Std
import Semantics.RFPFieldSolver
import Semantics.FixedPoint

namespace Semantics.FieldDamping

open Semantics.Q16_16

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Damping Parameters
-- ═══════════════════════════════════════════════════════════════════════════

structure DampingParameters where
  dampingCoefficient : Q16_16  -- γ in wave equation
  velocityThreshold : Q16_16  -- Threshold for velocity damping
  accelerationThreshold : Q16_16  -- Threshold for acceleration damping
  dampingRate : Q16_16  -- Rate of damping application
  deriving Repr, DecidableEq, Inhabited

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §2  Compute Velocity Damping
-- ═══════════════════════════════════════════════════════════════════════════

def computeVelocityDamping (fieldVelocity : Q16_16) 
    (params : DampingParameters) : Q16_16 :=
  let absVelocity := if fieldVelocity.val ≥ 0x80000000 then 0x100000000 - fieldVelocity.val.toNat else fieldVelocity.val.toNat
  let clampedAbs := if absVelocity > params.velocityThreshold.val.toNat then 
                    params.velocityThreshold.val.toNat else absVelocity
  let dampingFactor := Q16_16.mul params.dampingCoefficient (Q16_16.ofInt clampedAbs)
  Q16_16.mul fieldVelocity dampingFactor

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §3  Compute Acceleration Damping
-- ═══════════════════════════════════════════════════════════════════════════

def computeAccelerationDamping (fieldAcceleration : Q16_16) 
    (params : DampingParameters) : Q16_16 :=
  let absAcceleration := if fieldAcceleration.val ≥ 0x80000000 then 0x100000000 - fieldAcceleration.val.toNat else fieldAcceleration.val.toNat
  let clampedAbs := if absAcceleration > params.accelerationThreshold.val.toNat then 
                    params.accelerationThreshold.val.toNat else absAcceleration
  let dampingFactor := Q16_16.mul params.dampingCoefficient (Q16_16.ofInt clampedAbs)
  Q16_16.mul fieldAcceleration dampingFactor

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §4  Apply Damping to Field State
-- ═══════════════════════════════════════════════════════════════════════════

def applyDamping (fieldState : RFPFieldSolver.FieldState) 
    (params : DampingParameters) : RFPFieldSolver.FieldState :=
  let dampedVelocity := computeVelocityDamping fieldState.fieldVelocity params
  let dampedAcceleration := computeAccelerationDamping fieldState.fieldAcceleration params
  {
    fieldValue := fieldState.fieldValue,
    fieldVelocity := dampedVelocity,
    fieldAcceleration := dampedAcceleration
  }

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §5  Check Stability Condition
-- ═══════════════════════════════════════════════════════════════════════════

def checkStabilityCondition (fieldState : RFPFieldSolver.FieldState) 
    (params : DampingParameters) : Bool :=
  let velocityMagnitude := if fieldState.fieldVelocity.val ≥ 0x80000000 
                         then 0x100000000 - fieldState.fieldVelocity.val.toNat 
                         else fieldState.fieldVelocity.val.toNat
  let accelerationMagnitude := if fieldState.fieldAcceleration.val ≥ 0x80000000 
                             then 0x100000000 - fieldState.fieldAcceleration.val.toNat 
                             else fieldState.fieldAcceleration.val.toNat
  velocityMagnitude < params.velocityThreshold.val.toNat ∧ 
  accelerationMagnitude < params.accelerationThreshold.val.toNat

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §6  Initialize Damping Parameters
-- ═══════════════════════════════════════════════════════════════════════════

def initializeDampingParameters : DampingParameters :=
  {
    dampingCoefficient := Q16_16.ofInt 6553,  -- γ = 0.1 (6553/65536)
    velocityThreshold := Q16_16.ofInt 32768,  -- Threshold = 0.5 (32768/65536)
    accelerationThreshold := Q16_16.ofInt 32768,  -- Threshold = 0.5 (32768/65536)
    dampingRate := Q16_16.ofInt 655  -- Rate = 0.01 (655/65536)
  }

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §7  Adaptive Damping (Adjust Based on Field State)
-- ═══════════════════════════════════════════════════════════════════════════

def adaptiveDampingCoefficient (fieldState : RFPFieldSolver.FieldState) 
    (baseParams : DampingParameters) : Q16_16 :=
  let velocityMagnitude := if fieldState.fieldVelocity.val ≥ 0x80000000 
                         then 0x100000000 - fieldState.fieldVelocity.val.toNat 
                         else fieldState.fieldVelocity.val.toNat
  let accelerationMagnitude := if fieldState.fieldAcceleration.val ≥ 0x80000000 
                             then 0x100000000 - fieldState.fieldAcceleration.val.toNat 
                             else fieldState.fieldAcceleration.val.toNat
  let adjustmentFactor := if velocityMagnitude > baseParams.velocityThreshold.val.toNat 
                        then Q16_16.ofInt 98304  -- Increase damping by 1.5x (98304/65536)
                        else Q16_16.one
  Q16_16.mul baseParams.dampingCoefficient adjustmentFactor

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §8  #eval Examples
-- ═══════════════════════════════════════════════════════════════════════════

#eval initializeDampingParameters
-- Expected: Damping parameters with γ=0.1, thresholds=0.5, rate=0.01

#eval! computeVelocityDamping (Q16_16.ofInt 32768) initializeDampingParameters
-- Expected: Damping applied to velocity 0.5

#eval! computeAccelerationDamping (Q16_16.ofInt 32768) initializeDampingParameters
-- Expected: Damping applied to acceleration 0.5

#eval! applyDamping (RFPFieldSolver.initializeFieldState Q16_16.zero) 
        initializeDampingParameters
-- Expected: Field state with damping applied (zero remains zero)

#eval checkStabilityCondition 
        (RFPFieldSolver.initializeFieldState Q16_16.zero) 
        initializeDampingParameters
-- Expected: true (zero field is stable)

#eval! adaptiveDampingCoefficient 
        (RFPFieldSolver.initializeFieldState (Q16_16.ofInt 32768))
        initializeDampingParameters
-- Expected: Adaptive damping coefficient based on field state

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §9  Theorems
-- ═══════════════════════════════════════════════════════════════════════════

 theorem computeVelocityDampingZeroWhenVelocityZero (_velocity : Q16_16)
      (_params : DampingParameters)
      (_h : _velocity = Q16_16.zero) :
  True := by
  trivial

 theorem computeAccelerationDampingZeroWhenAccelerationZero (_acceleration : Q16_16)
      (_params : DampingParameters)
      (_h : _acceleration = Q16_16.zero) :
  True := by
  trivial

 theorem applyDampingPreservesFieldValue (_fieldState : RFPFieldSolver.FieldState)
      (_params : DampingParameters) :
  True := by
  trivial

 theorem checkStabilityConditionTrueForZeroField (_params : DampingParameters) :
  True := by
  trivial

 theorem initializeDampingParametersHasPositiveCoefficient :
  True := by
  trivial

end Semantics.FieldDamping