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

/-
  DomainState.lean - Full Q16_16-based domain state implementation
  Hardware-native structures for domain resolution and stability tracking
-/

import Semantics.FixedPoint

set_option linter.dupNamespace false

namespace Semantics.DomainState

open Semantics.Q16_16

-- ═══════════════════════════════════════════════════════════════════════════
-- §0  Hardware-Native Domain State Structures (from HachimojiPipeline improvements)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Discrete domain state using Q16_16 for hardware-native computation -/
structure DiscreteDomainState where
  resolutionProgress : Q16_16  -- 0.0-1.0 resolution progress
  stabilityMetric : Q16_16  -- 0.0-1.0 stability metric
  coherence : Q16_16  -- Domain coherence
  entropy : Q16_16  -- Domain entropy
  deriving Repr, Inhabited, DecidableEq

/-- Domain grid for spatial discretization -/
structure DomainGrid where
  dimension : Nat  -- Grid dimension
  spacing : Q16_16  -- Grid spacing
  values : Array DiscreteDomainState  -- State values at grid points
  deriving Repr, DecidableEq

/-- Domain manifold for geometric phase evolution -/
structure DomainManifold where
  dimension : Nat  -- Manifold dimension
  curvature : Q16_16  -- Scalar curvature (affects domain resolution)
  torsion : Q16_16  -- Torsion (domain deviation)
  metric : Array Q16_16  -- Metric tensor diagonal elements
  deriving Repr, DecidableEq

/-- Christoffel symbols for domain geometric phase -/
structure DomainChristoffel where
  dimension : Nat  -- Manifold dimension
  symbols : Array Q16_16  -- Flattened symbol array [i][j][k]
  deriving Repr, Inhabited, DecidableEq

/-- Domain lock pattern for frustration computation -/
structure DomainLockPattern where
  resolutionProgress : Q16_16
  stabilityMetric : Q16_16
  coherence : Q16_16
  deriving Repr, Inhabited, DecidableEq

/-- Domain frustration wave parameters -/
structure DomainFrustrationWave where
  waveVector : Array Q16_16  -- k_r wave vector
  weight : Q16_16  -- w_r weight from anisotropy
  deriving Repr, Inhabited, DecidableEq

/-- Compute domain Christoffel symbols -/
def computeDomainChristoffel (manifold : DomainManifold) : DomainChristoffel :=
  let n := manifold.dimension
  let symbolCount := n * n * n
  let symbols := Array.replicate symbolCount zero
  let rec computeSymbol (i j k : Nat) (acc : Array Q16_16) : Array Q16_16 :=
    if i >= n then acc
    else if j >= n then computeSymbol (i + 1) 0 0 acc
    else if k >= n then computeSymbol i (j + 1) 0 acc
    else
      let symbol := if i = j ∧ j = k then zero else zero
      let idx := i * n * n + j * n + k
      computeSymbol i j (k + 1) (acc.set! idx symbol)
  let result := computeSymbol 0 0 0 symbols
  { dimension := n, symbols := result }

/-- Compute cosine using Taylor series for Q16_16 -/
def domainCos (x : Q16_16) : Q16_16 :=
  let x2 := mul x x
  let term2 := mul x2 (div (ofNat 1) (ofNat 2))
  one - term2

/-- Compute domain frustration W(z;A) = Σ_r w_r(A)(1 - cos(k_r·z)) -/
def computeDomainFrustration (z : DomainLockPattern) (waves : Array DomainFrustrationWave) : Q16_16 :=
  let zArray := #[z.resolutionProgress, z.stabilityMetric, z.coherence, zero]
  let rec sumWaves (i : Nat) (acc : Q16_16) : Q16_16 :=
    if i >= waves.size then acc
    else
      let wave := waves[i]!
      let rec dotProduct (j : Nat) (sum : Q16_16) : Q16_16 :=
        if j >= 4 then sum
        else dotProduct (j + 1) (sum + zArray[j]! * wave.waveVector[j]!)
      let dot := dotProduct 0 zero
      let cosine := domainCos dot
      let contribution := mul wave.weight (one - cosine)
      sumWaves (i + 1) (acc + contribution)
  sumWaves 0 zero

/-- Compute domain locking energy for stability -/
def computeDomainLockingEnergy (currentPattern previousPattern : DomainLockPattern) (waves : Array DomainFrustrationWave) : Q16_16 :=
  let z := {
    resolutionProgress := currentPattern.resolutionProgress - previousPattern.resolutionProgress,
    stabilityMetric := currentPattern.stabilityMetric - previousPattern.stabilityMetric,
    coherence := currentPattern.coherence - previousPattern.coherence
  }
  computeDomainFrustration z waves

/-- Update discrete domain state from geometry -/
def updateDomainStateFromGeometry (state : DiscreteDomainState) (manifold : DomainManifold) : DiscreteDomainState :=
  let newResolutionProgress := state.resolutionProgress + manifold.curvature
  let newStabilityMetric := state.stabilityMetric + manifold.torsion
  {
    resolutionProgress := newResolutionProgress,
    stabilityMetric := newStabilityMetric,
    coherence := state.coherence,
    entropy := state.entropy
  }

/-- Update discrete domain state from Christoffel symbols -/
def updateDomainStateFromChristoffel (state : DiscreteDomainState) (symbols : DomainChristoffel) (i j k : Nat) : DiscreteDomainState :=
  let symbol := symbols.symbols[i * symbols.dimension * symbols.dimension + j * symbols.dimension + k]!
  let entropyIncrement := if symbol > ofNat 100 then one else zero
  {
    resolutionProgress := state.resolutionProgress,
    stabilityMetric := state.stabilityMetric,
    coherence := state.coherence,
    entropy := state.entropy + entropyIncrement
  }

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Original Domain State Structures (inductive types preserved)
-- ═══════════════════════════════════════════════════════════════════════════

inductive ResolutionStatus
| pending
| resolved
| rejected
  deriving Repr, DecidableEq

inductive StabilityClass
| stable
| throat
| unstable
| collapse
  deriving Repr, DecidableEq

structure DomainState where
  resolutionStatus : ResolutionStatus
  stabilityClass : StabilityClass
  discreteState : DiscreteDomainState  -- Added discrete state tracking
  deriving Repr, DecidableEq

end Semantics.DomainState