Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/MultiSurfacePacker.lean

import Std
import Semantics.FixedPoint
import Semantics.DeltaGCLCompression
import Semantics.GoldenAngleEncoding

namespace Semantics.MultiSurfacePacker

open Semantics.Q16_16
open Semantics.DeltaGCLCompression
open Semantics.GoldenAngleEncoding

structure DeltaSurfaceCost where
  deltaL1 : Q16_16
  blockCount : Nat
  avgCompressibility : Q16_16
  deriving Repr, Inhabited, DecidableEq

structure SpectralSurfaceCost where
  sampleCount : Q16_16
  coherence : Q16_16
  spectralEnergy : Q16_16
  deriving Repr, Inhabited, DecidableEq

structure ProgramSurfaceCost where
  descriptionLength : Q16_16
  complexity : Q16_16
  codonCount : Nat
  deriving Repr, Inhabited, DecidableEq

structure MultiSurfaceLagrangian where
  deltaCost : Q16_16
  spectralCost : Q16_16
  programCost : Q16_16
  alpha : Q16_16
  beta : Q16_16
  total : Q16_16
  deriving Repr, Inhabited, DecidableEq

def computeLagrangian (delta : DeltaSurfaceCost) (spectral : SpectralSurfaceCost)
    (program : ProgramSurfaceCost) (alpha beta : Q16_16) : MultiSurfaceLagrangian :=
  let spectralWeighted := Q16_16.mul alpha spectral.sampleCount
  let programWeighted := Q16_16.mul beta program.descriptionLength
  let total := Q16_16.add delta.deltaL1 (Q16_16.add spectralWeighted programWeighted)
  { deltaCost := delta.deltaL1
    spectralCost := spectralWeighted
    programCost := programWeighted
    alpha := alpha
    beta := beta
    total := total }

def coherenceOverlap (samplesA samplesB : List Q16_16) : Q16_16 :=
  if samplesA.isEmpty ∨ samplesB.isEmpty then
    Q16_16.ofNat 0
  else
    let m := min samplesA.length samplesB.length
    let commonA := samplesA.take m
    let commonB := samplesB.take m
    if m = 0 then
      Q16_16.ofNat 0
    else
      let meanA := Q16_16.ofNat (commonA.foldl (· + ·) 0 / m)
      let meanB := Q16_16.ofNat (commonB.foldl (· + ·) 0 / m)
      let dot := commonA.foldlWithIndex (fun acc i a =>
        let aCentered := Q16_16.sub a meanA
        let bCentered := Q16_16.sub commonB[i]! meanB
        Q16_16.add acc (Q16_16.mul aCentered bCentered)) (Q16_16.ofNat 0)
      let normA := commonA.foldl (fun acc a =>
        let aC := Q16_16.sub a meanA
        Q16_16.add acc (Q16_16.mul aC aC)) (Q16_16.ofNat 0)
      let normB := commonB.foldl (fun acc b =>
        let bC := Q16_16.sub b meanB
        Q16_16.add acc (Q16_16.mul bC bC)) (Q16_16.ofNat 0)
      if normA.val = 0 ∧ normB.val = 0 then
        Q16_16.ofNat 65536
      else
        let denom := Q16_16.mul normA normB
        if denom.val = 0 then
          Q16_16.ofNat 0
        else
          Q16_16.div (Q16_16.mul dot dot) denom

def coherenceGate (overlapSq : Q16_16) (epsilon : Q16_16) : Bool :=
  let threshold := Q16_16.sub (Q16_16.ofNat 65536) epsilon
  overlapSq.val ≥ threshold.val

def GCDecision where
  accept : Bool
  reject : Bool
  hold : Bool
  quarantine : Bool
  deriving Repr, Inhabited, DecidableEq

def gcclSwapGate (oldCost newCost reconRisk : Q16_16) : GCDecision :=
  let improvement := if oldCost.val > newCost.val then
    Q16_16.sub oldCost newCost
  else
    Q16_16.ofNat 0
  let admissible := improvement.val ≤ reconRisk.val
  { accept := admissible
    reject := ¬admissible
    hold := ¬admissible
    quarantine := False }

structure MultiSurfaceReceipt where
  schema : String := "multi_surface_packing_v1"
  inputSize : Nat
  deltaCost : Q16_16
  spectralCost : Q16_16
  programCost : Q16_16
  totalLagrangian : Q16_16
  coherencePassed : Bool
  gcclPassed : Bool
  decision : String
  compressedSize : Nat
  compressionRatio : Q16_16
  claimBoundary : String := "multi-surface-packing-lean-core"
  deriving Repr, Inhabited, DecidableEq

def finalizeReceipt (receipt : MultiSurfaceReceipt) : MultiSurfaceReceipt :=
  receipt

theorem coherenceGateAcceptsIdentical :
    coherenceGate (Q16_16.ofNat 65536) (Q16_16.ofNat 3277) = true := by
  simp [coherenceGate, Q16_16.sub, Q16_16.ofNat]
  decide

theorem coherenceGateRejectsOrthogonal :
    coherenceGate (Q16_16.ofNat 0) (Q16_16.ofNat 3277) = false := by
  simp [coherenceGate, Q16_16.sub, Q16_16.ofNat]
  decide

theorem gcclRejectsExpansion :
    gcclSwapGate (Q16_16.ofNat 100) (Q16_16.ofNat 200) (Q16_16.ofNat 500) =
    { accept := false, reject := true, hold := true, quarantine := false } := by
  simp [gcclSwapGate, Q16_16.sub, Q16_16.mul, Q16_16.ofNat]
  decide

def exampleDelta : DeltaSurfaceCost := {
  deltaL1 := Q16_16.ofNat 12800
  blockCount := 4
  avgCompressibility := Q16_16.ofNat 32768
}

def exampleSpectral : SpectralSurfaceCost := {
  sampleCount := Q16_16.ofNat 256
  coherence := Q16_16.ofNat 55705
  spectralEnergy := Q16_16.ofNat 65536
}

def exampleProgram : ProgramSurfaceCost := {
  descriptionLength := Q16_16.ofNat 500
  complexity := Q16_16.ofNat 29491
  codonCount := 150
}

#eval exampleDelta
#eval exampleSpectral
#eval exampleProgram
#eval computeLagrangian exampleDelta exampleSpectral exampleProgram (Q16_16.ofNat 6554) (Q16_16.ofNat 3277)
#eval coherenceGateAcceptsIdentical
#eval coherenceGateRejectsOrthogonal
#eval gcclRejectsExpansion

end Semantics.MultiSurfacePacker