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77 lines
2.3 KiB
Text
77 lines
2.3 KiB
Text
import Semantics.FixedPoint
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namespace Semantics.VideoPhysics
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open Lean Semantics.Q16_16
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/-- Standard fixed-point scalar -/
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abbrev Scalar := Q16_16
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/--
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OISC-SLUG3 Instruction Set:
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27 ternary opcodes driving the transition of Braid coordinates
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on the NUVMap pixel surface.
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-/
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inductive Instruction
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| sub : Instruction -- Subtract
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| pause : Instruction -- Pause
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| add : Instruction -- Add
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deriving Repr, BEq
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/-- One SLUG3 codon is 3 ternary instructions -/
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structure Codon where
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i1 : Instruction
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i2 : Instruction
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i3 : Instruction
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deriving Repr, BEq
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/--
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Video Weird Machine (VWM) State:
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Repurposing the H.264 pipeline for deterministic entropy generation.
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-/
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structure VWMState where
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manifold_sigma : Scalar
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peaks_spectral : Array Scalar
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hdmi_residual : Scalar
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frame_index : Nat
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deriving Repr
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instance : ToJson VWMState where
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toJson s := Json.mkObj [
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("manifold_sigma", toJson s.manifold_sigma),
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("peaks_spectral", toJson s.peaks_spectral),
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("hdmi_residual", toJson s.hdmi_residual),
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("frame_index", toJson s.frame_index)
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]
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instance : FromJson VWMState where
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fromJson? j := do
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let sigma ← (← j.getObjVal? "manifold_sigma").getObjVal? "val" >>= fun v => v.getNat?
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let peaks ← (← j.getObjVal? "peaks_spectral").getArr?
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let residual ← (← j.getObjVal? "hdmi_residual").getObjVal? "val" >>= fun v => v.getNat?
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let frame ← (← j.getObjVal? "frame_index").getNat?
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pure {
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manifold_sigma := ⟨sigma.toUInt32⟩,
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peaks_spectral := peaks.map (fun p => match fromJson? p with | .ok q => q | .error _ => zero),
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hdmi_residual := ⟨residual.toUInt32⟩,
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frame_index := frame
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}
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/--
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Model 141 Master Equation:
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Σ_{t+1} = D_SNN(Φ_120Hz ⊗ (Peaks(S_η) ⊕ R_HDMI))
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-/
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def masterEquation (state : VWMState) : Scalar :=
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-- Φ_120Hz is represented as a scaling factor in Q16.16
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let phi := ofInt 120
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let spectral_sum := state.peaks_spectral.foldl (fun acc p => acc + p) zero
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let inner := spectral_sum + state.hdmi_residual
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phi * inner
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/-- Transition function for the Video Weird Machine -/
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def step (state : VWMState) (_instr : List Codon) : VWMState :=
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{ state with
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manifold_sigma := masterEquation state,
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frame_index := state.frame_index + 1 }
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end Semantics.VideoPhysics
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