import Semantics.FixedPoint

namespace Semantics.VideoPhysics

open Lean Semantics.Q16_16

/-- Standard fixed-point scalar -/
abbrev Scalar := Q16_16

/--
  OISC-SLUG3 Instruction Set:
  27 ternary opcodes driving the transition of Braid coordinates
  on the NUVMap pixel surface.
-/
inductive Instruction
  | sub   : Instruction -- Subtract
  | pause : Instruction -- Pause
  | add   : Instruction -- Add
  deriving Repr, BEq

/-- One SLUG3 codon is 3 ternary instructions -/
structure Codon where
  i1 : Instruction
  i2 : Instruction
  i3 : Instruction
  deriving Repr, BEq

/-- 
  Video Weird Machine (VWM) State:
  Repurposing the H.264 pipeline for deterministic entropy generation.
-/
structure VWMState where
  manifold_sigma : Scalar
  peaks_spectral : Array Scalar
  hdmi_residual  : Scalar
  frame_index    : Nat
  deriving Repr

instance : ToJson VWMState where
  toJson s := Json.mkObj [
    ("manifold_sigma", toJson s.manifold_sigma),
    ("peaks_spectral", toJson s.peaks_spectral),
    ("hdmi_residual", toJson s.hdmi_residual),
    ("frame_index", toJson s.frame_index)
  ]

instance : FromJson VWMState where
  fromJson? j := do
    let sigma ← (← j.getObjVal? "manifold_sigma").getObjVal? "val" >>= fun v => v.getNat?
    let peaks ← (← j.getObjVal? "peaks_spectral").getArr?
    let residual ← (← j.getObjVal? "hdmi_residual").getObjVal? "val" >>= fun v => v.getNat?
    let frame ← (← j.getObjVal? "frame_index").getNat?
    pure { 
      manifold_sigma := ⟨sigma.toUInt32⟩,
      peaks_spectral := peaks.map (fun p => match fromJson? p with | .ok q => q | .error _ => zero),
      hdmi_residual := ⟨residual.toUInt32⟩,
      frame_index := frame
    }

/-- 
  Model 141 Master Equation:
  Σ_{t+1} = D_SNN(Φ_120Hz ⊗ (Peaks(S_η) ⊕ R_HDMI))
-/
def masterEquation (state : VWMState) : Scalar :=
  -- Φ_120Hz is represented as a scaling factor in Q16.16
  let phi := ofInt 120
  let spectral_sum := state.peaks_spectral.foldl (fun acc p => acc + p) zero
  let inner := spectral_sum + state.hdmi_residual
  phi * inner

/-- Transition function for the Video Weird Machine -/
def step (state : VWMState) (_instr : List Codon) : VWMState :=
  { state with 
    manifold_sigma := masterEquation state,
    frame_index := state.frame_index + 1 }

end Semantics.VideoPhysics
