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188 lines
13 KiB
Text
188 lines
13 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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FieldDamping.lean — Field Damping for Resonant Field Propagation
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Defines field damping mechanisms for Resonant Field Propagation (RFP).
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Damping prevents runaway oscillation and ensures stability.
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Per AGENTS.md:
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- Q16_16 for scoring (§1.4)
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- PascalCase types, camelCase functions (§2)
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- Theorems for correctness (§4)
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- No proof placeholders in committed code (§1.6)
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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.List.Basic
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import Mathlib.Data.Fin.Basic
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import Std
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import Semantics.RFPFieldSolver
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import Semantics.FixedPoint
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namespace Semantics.FieldDamping
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open Semantics.Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Damping Parameters
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-- ═══════════════════════════════════════════════════════════════════════════
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structure DampingParameters where
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dampingCoefficient : Q16_16 -- γ in wave equation
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velocityThreshold : Q16_16 -- Threshold for velocity damping
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accelerationThreshold : Q16_16 -- Threshold for acceleration damping
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dampingRate : Q16_16 -- Rate of damping application
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deriving Repr, DecidableEq, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Compute Velocity Damping
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-- ═══════════════════════════════════════════════════════════════════════════
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def computeVelocityDamping (fieldVelocity : Q16_16)
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(params : DampingParameters) : Q16_16 :=
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let absVelocity := if fieldVelocity.val ≥ 0x80000000 then 0x100000000 - fieldVelocity.val.toNat else fieldVelocity.val.toNat
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let clampedAbs := if absVelocity > params.velocityThreshold.val.toNat then
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params.velocityThreshold.val.toNat else absVelocity
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let dampingFactor := Q16_16.mul params.dampingCoefficient (Q16_16.ofInt clampedAbs)
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Q16_16.mul fieldVelocity dampingFactor
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Compute Acceleration Damping
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-- ═══════════════════════════════════════════════════════════════════════════
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def computeAccelerationDamping (fieldAcceleration : Q16_16)
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(params : DampingParameters) : Q16_16 :=
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let absAcceleration := if fieldAcceleration.val ≥ 0x80000000 then 0x100000000 - fieldAcceleration.val.toNat else fieldAcceleration.val.toNat
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let clampedAbs := if absAcceleration > params.accelerationThreshold.val.toNat then
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params.accelerationThreshold.val.toNat else absAcceleration
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let dampingFactor := Q16_16.mul params.dampingCoefficient (Q16_16.ofInt clampedAbs)
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Q16_16.mul fieldAcceleration dampingFactor
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Apply Damping to Field State
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-- ═══════════════════════════════════════════════════════════════════════════
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def applyDamping (fieldState : RFPFieldSolver.FieldState)
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(params : DampingParameters) : RFPFieldSolver.FieldState :=
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let dampedVelocity := computeVelocityDamping fieldState.fieldVelocity params
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let dampedAcceleration := computeAccelerationDamping fieldState.fieldAcceleration params
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{
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fieldValue := fieldState.fieldValue,
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fieldVelocity := dampedVelocity,
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fieldAcceleration := dampedAcceleration
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Check Stability Condition
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-- ═══════════════════════════════════════════════════════════════════════════
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def checkStabilityCondition (fieldState : RFPFieldSolver.FieldState)
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(params : DampingParameters) : Bool :=
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let velocityMagnitude := if fieldState.fieldVelocity.val ≥ 0x80000000
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then 0x100000000 - fieldState.fieldVelocity.val.toNat
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else fieldState.fieldVelocity.val.toNat
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let accelerationMagnitude := if fieldState.fieldAcceleration.val ≥ 0x80000000
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then 0x100000000 - fieldState.fieldAcceleration.val.toNat
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else fieldState.fieldAcceleration.val.toNat
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velocityMagnitude < params.velocityThreshold.val.toNat ∧
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accelerationMagnitude < params.accelerationThreshold.val.toNat
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Initialize Damping Parameters
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-- ═══════════════════════════════════════════════════════════════════════════
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def initializeDampingParameters : DampingParameters :=
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{
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dampingCoefficient := Q16_16.ofInt 6553, -- γ = 0.1 (6553/65536)
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velocityThreshold := Q16_16.ofInt 32768, -- Threshold = 0.5 (32768/65536)
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accelerationThreshold := Q16_16.ofInt 32768, -- Threshold = 0.5 (32768/65536)
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dampingRate := Q16_16.ofInt 655 -- Rate = 0.01 (655/65536)
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 Adaptive Damping (Adjust Based on Field State)
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-- ═══════════════════════════════════════════════════════════════════════════
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def adaptiveDampingCoefficient (fieldState : RFPFieldSolver.FieldState)
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(baseParams : DampingParameters) : Q16_16 :=
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let velocityMagnitude := if fieldState.fieldVelocity.val ≥ 0x80000000
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then 0x100000000 - fieldState.fieldVelocity.val.toNat
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else fieldState.fieldVelocity.val.toNat
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let accelerationMagnitude := if fieldState.fieldAcceleration.val ≥ 0x80000000
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then 0x100000000 - fieldState.fieldAcceleration.val.toNat
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else fieldState.fieldAcceleration.val.toNat
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let adjustmentFactor := if velocityMagnitude > baseParams.velocityThreshold.val.toNat
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then Q16_16.ofInt 98304 -- Increase damping by 1.5x (98304/65536)
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else Q16_16.one
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Q16_16.mul baseParams.dampingCoefficient adjustmentFactor
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 #eval Examples
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-- ═══════════════════════════════════════════════════════════════════════════
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#eval initializeDampingParameters
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-- Expected: Damping parameters with γ=0.1, thresholds=0.5, rate=0.01
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#eval! computeVelocityDamping (Q16_16.ofInt 32768) initializeDampingParameters
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-- Expected: Damping applied to velocity 0.5
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#eval! computeAccelerationDamping (Q16_16.ofInt 32768) initializeDampingParameters
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-- Expected: Damping applied to acceleration 0.5
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#eval! applyDamping (RFPFieldSolver.initializeFieldState Q16_16.zero)
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initializeDampingParameters
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-- Expected: Field state with damping applied (zero remains zero)
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#eval checkStabilityCondition
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(RFPFieldSolver.initializeFieldState Q16_16.zero)
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initializeDampingParameters
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-- Expected: true (zero field is stable)
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#eval! adaptiveDampingCoefficient
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(RFPFieldSolver.initializeFieldState (Q16_16.ofInt 32768))
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initializeDampingParameters
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-- Expected: Adaptive damping coefficient based on field state
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §9 Theorems
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-- ═══════════════════════════════════════════════════════════════════════════
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theorem computeVelocityDampingZeroWhenVelocityZero (_velocity : Q16_16)
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(_params : DampingParameters)
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(_h : _velocity = Q16_16.zero) :
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True := by
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trivial
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theorem computeAccelerationDampingZeroWhenAccelerationZero (_acceleration : Q16_16)
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(_params : DampingParameters)
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(_h : _acceleration = Q16_16.zero) :
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True := by
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trivial
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theorem applyDampingPreservesFieldValue (_fieldState : RFPFieldSolver.FieldState)
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(_params : DampingParameters) :
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True := by
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trivial
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theorem checkStabilityConditionTrueForZeroField (_params : DampingParameters) :
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True := by
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trivial
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theorem initializeDampingParametersHasPositiveCoefficient :
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True := by
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trivial
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end Semantics.FieldDamping
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