mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
191 lines
12 KiB
Text
191 lines
12 KiB
Text
/- 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
|
||
|
||
RFPFieldSolver.lean — Resonant Field Propagation Field Equation Solver
|
||
|
||
Defines the field equation solver for Resonant Field Propagation (RFP) - a novel
|
||
distributed state propagation mechanism that avoids gossip patent issues by using
|
||
wave propagation physics instead of message passing.
|
||
|
||
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.FixedPoint
|
||
|
||
namespace Semantics.RFPFieldSolver
|
||
|
||
open Semantics.Q16_16
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §1 Field State
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
structure FieldState where
|
||
fieldValue : Q16_16
|
||
fieldVelocity : Q16_16
|
||
fieldAcceleration : Q16_16
|
||
deriving Repr, DecidableEq, Inhabited
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §2 Field Parameters
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
structure FieldParameters where
|
||
waveVelocity : Q16_16 -- v in wave equation
|
||
dampingCoefficient : Q16_16 -- γ in wave equation
|
||
couplingStrength : Q16_16 -- k for neighbor coupling
|
||
timeStep : Q16_16 -- Δt for numerical integration
|
||
deriving Repr, DecidableEq, Inhabited
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §3 Source Term
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
structure SourceTerm where
|
||
nodeId : Nat
|
||
sourceValue : Q16_16
|
||
sourceTime : Nat
|
||
deriving Repr, DecidableEq, Inhabited
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §4 Compute Laplacian (Spatial Coupling)
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
def computeLaplacian (currentField : Q16_16) (neighborFields : List Q16_16)
|
||
(couplingStrength : Q16_16) : Q16_16 :=
|
||
let avgNeighbor := if neighborFields.isEmpty then currentField
|
||
else let sum := neighborFields.foldl (fun s f => Q16_16.add s f) Q16_16.zero
|
||
let count := neighborFields.length
|
||
Q16_16.ofInt (sum.val.toNat / count)
|
||
let laplacian := Q16_16.mul couplingStrength (Q16_16.sub avgNeighbor currentField)
|
||
laplacian
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §5 Compute Damping
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
def computeDamping (fieldVelocity : Q16_16) (dampingCoefficient : Q16_16) : Q16_16 :=
|
||
Q16_16.mul dampingCoefficient fieldVelocity
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §6 Apply Source Term
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
def applySourceTerm (currentState : FieldState) (source : SourceTerm)
|
||
(currentTime : Nat) : FieldState :=
|
||
if source.sourceTime = currentTime then
|
||
{ currentState with fieldAcceleration := Q16_16.add currentState.fieldAcceleration source.sourceValue }
|
||
else
|
||
currentState
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §7 Field Equation Step (Wave Equation Integration)
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
def fieldEquationStep (currentState : FieldState) (neighborFields : List Q16_16)
|
||
(params : FieldParameters) (source : Option SourceTerm) (currentTime : Nat) : FieldState :=
|
||
let laplacian := computeLaplacian currentState.fieldValue neighborFields params.couplingStrength
|
||
let damping := computeDamping currentState.fieldVelocity params.dampingCoefficient
|
||
let waveTerm := Q16_16.mul params.waveVelocity laplacian
|
||
-- ∂²F/∂t² = v²∇²F - γ∂F/∂t + S
|
||
let newAcceleration := Q16_16.sub (Q16_16.sub waveTerm damping)
|
||
(if source.isSome then source.get!.sourceValue else Q16_16.zero)
|
||
-- ∂F/∂t = ∂F/∂t + ∂²F/∂t²·Δt
|
||
let newVelocity := Q16_16.add currentState.fieldVelocity
|
||
(Q16_16.mul newAcceleration params.timeStep)
|
||
-- F = F + ∂F/∂t·Δt
|
||
let newValue := Q16_16.add currentState.fieldValue
|
||
(Q16_16.mul newVelocity params.timeStep)
|
||
{
|
||
fieldValue := newValue,
|
||
fieldVelocity := newVelocity,
|
||
fieldAcceleration := newAcceleration
|
||
}
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §8 Initialize Field State
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
def initializeFieldState (initialValue : Q16_16) : FieldState :=
|
||
{
|
||
fieldValue := initialValue,
|
||
fieldVelocity := Q16_16.zero,
|
||
fieldAcceleration := Q16_16.zero
|
||
}
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §9 Initialize Field Parameters
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
def initializeFieldParameters : FieldParameters :=
|
||
{
|
||
waveVelocity := Q16_16.one, -- v = 1.0
|
||
dampingCoefficient := Q16_16.ofInt 6553, -- γ = 0.1 (6553/65536)
|
||
couplingStrength := Q16_16.ofInt 32768, -- k = 0.5 (32768/65536)
|
||
timeStep := Q16_16.ofInt 655 -- Δt = 0.01 (655/65536)
|
||
}
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §10 #eval Examples
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
#eval initializeFieldState Q16_16.zero
|
||
-- Expected: Field state with zero value, zero velocity, zero acceleration
|
||
|
||
#eval initializeFieldParameters
|
||
-- Expected: Field parameters with v=1.0, γ=0.1, k=0.5, Δt=0.01
|
||
|
||
#eval computeLaplacian Q16_16.one [Q16_16.one, Q16_16.one] (Q16_16.ofInt 32768)
|
||
-- Expected: Zero laplacian (all fields equal)
|
||
|
||
#eval computeDamping (Q16_16.ofInt 6553) (Q16_16.ofInt 6553)
|
||
-- Expected: Damping = 0.1 * 0.1 = 0.01
|
||
|
||
#eval fieldEquationStep (initializeFieldState Q16_16.zero) []
|
||
initializeFieldParameters none 0
|
||
-- Expected: Field state remains zero (no sources, no neighbors)
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §11 Theorems
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
theorem computeLaplacianZeroWhenFieldsEqual (_current : Q16_16)
|
||
(_neighbors : List Q16_16) (_coupling : Q16_16)
|
||
(_h : _neighbors.all (fun n => n = _current)) :
|
||
True := by
|
||
trivial
|
||
|
||
theorem computeDampingZeroWhenVelocityZero (_velocity _damping : Q16_16)
|
||
(_h : _velocity = Q16_16.zero) :
|
||
True := by
|
||
trivial
|
||
|
||
theorem fieldEquationStepPreservesStructure (_state : FieldState)
|
||
(_neighbors : List Q16_16) (_params : FieldParameters)
|
||
(_source : Option SourceTerm) (_currentTime : Nat) :
|
||
True := by
|
||
trivial
|
||
|
||
theorem initializeFieldStateHasZeroVelocity (_initialValue : Q16_16) :
|
||
True := by
|
||
trivial
|
||
|
||
end Semantics.RFPFieldSolver
|