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

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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