/-
  FieldSolver.lean - Torsion Field Compression Solver
  Compliant with AGENTS.md Q16_16 bounds and minimal bind topology.
-/
import Semantics.Atoms
import Semantics.Bind

namespace Semantics.FieldSolver

/-- Fixed-point coordinate using project standard Q16.16 -/
abbrev Q16_16 := UInt32

namespace Q16_16
  def scale : Nat := 65536
  def maxNat : Nat := 4294967295

  def satFromNat (n : Nat) : Q16_16 :=
    if n > maxNat then UInt32.ofNat maxNat else UInt32.ofNat n

  def mul (x y : Q16_16) : Q16_16 :=
    satFromNat ((x.toNat * y.toNat) / scale)

  def add (x y : Q16_16) : Q16_16 :=
    satFromNat (x.toNat + y.toNat)

  def sub (x y : Q16_16) : Q16_16 :=
    if x.toNat < y.toNat then 0 else satFromNat (x.toNat - y.toNat)
end Q16_16

structure FieldSolverState where
  w : UInt32
  lambdaE : UInt32
  ell : UInt32
  eta : UInt32
  engramKey : UInt32
  activationHistorySum : UInt32
  historyCount : UInt32
deriving Repr, Inhabited, DecidableEq

def computeLaplacian (w : UInt32) (historyAvg : UInt32) : UInt32 :=
  let baseTorsion := ((w >>> 16) ^^^ (w >>> 8) ^^^ w) &&& 0xFF
  if historyAvg > 0 then (baseTorsion + historyAvg) / 2 else baseTorsion

def engramQuery (key : UInt32) (position : UInt32) : UInt32 :=
  (key ^^^ position ^^^ 0xDEADBEEF) >>> 24

def stabilityPenalty (w : UInt32) (historyAvg : UInt32) (lambdaStab : Q16_16) : Q16_16 :=
  if historyAvg == 0 then 0
  else
    let drift := if w > historyAvg then w - historyAvg else historyAvg - w
    let driftQ : Q16_16 := UInt32.ofNat ((drift.toNat * Q16_16.scale) / 0xFFFFFFFF)
    Q16_16.mul lambdaStab (Q16_16.mul driftQ driftQ)

def fieldInvariant (state : FieldSolverState) : String :=
  s!"w:{state.w},lambda:{state.lambdaE}"

/-- Informational cost over Torsion Field evaluation step -/
def informationalCost (left right : FieldSolverState) ( _metric  : Metric) : UInt32 :=
  let avgLeft := if left.historyCount > 0 then left.activationHistorySum / left.historyCount else 0
  let avgRight := if right.historyCount > 0 then right.activationHistorySum / right.historyCount else 0
  let tL := (computeLaplacian left.w avgLeft).toNat
  let tR := (computeLaplacian right.w avgRight).toNat
  let baseTorsionDiff := if tL < tR then tR - tL else tL - tR
  -- Cost is proportional to the gradient change, clamped to Q16.16 max
  Q16_16.satFromNat (baseTorsionDiff * Q16_16.scale)

def informationalBindEval (left right : FieldSolverState) ( _metric  : Metric) : Bind FieldSolverState FieldSolverState :=
  informationalBind left right  _metric  informationalCost fieldInvariant fieldInvariant

#eval informationalCost { w := 0x12345678, lambdaE := 256, ell := 4, eta := 16, engramKey := 0, activationHistorySum := 0, historyCount := 0 } { w := 0x12345679, lambdaE := 256, ell := 4, eta := 16, engramKey := 0, activationHistorySum := 0, historyCount := 0 } (Metric.euclidean)

end Semantics.FieldSolver