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

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import Semantics.PISTMachine
import Semantics.Functions.BracketedCalculus
namespace Semantics.PBACSSignal
open Semantics.Functions.BracketedCalculus
open Semantics.PISTMachine
/-! # PBACS REV3 — Signal Transport
Neutralized Specification.
Anchored to: linear/RES-2311
-/
/-- 1-bit output symbol. -/
abbrev Symbol := Bool
/-- PBACS Unified State Vector.
Refactored to align with PISTMachine nomenclature. -/
structure State where
phi : UInt32 -- L2 φ-accumulator
error : Int32 -- L1 Error accumulator
tension : UInt32 -- L4 Tension accumulator
phase : Phase -- L4 PIST Phase sort
lastSymbol : Symbol -- L1 Output symbol
bracket : BracketedDIAT -- L5 BracketedDIAT
deriving Repr, BEq, DecidableEq
namespace State
def default : State := {
phi := 0,
error := 0,
tension := 0,
phase := Phase.grounded,
lastSymbol := false,
bracket := BracketedDIAT.encode 0 0 0 0
}
/-- Step 1: Phi increment (Golden Ratio constant). -/
def nextPhi (phi : UInt32) : UInt32 :=
phi + 106070 -- ≈ 2^32 / φ^2
/-- Step 2: Threshold LUT lookup (simulated via MSB check). -/
def getThreshold (phi : UInt32) : Int32 :=
if phi >= 0x80000000 then 32768 else -32768
/-- Canonical Update Law (Steps 1-8).
v_t: Input sample in Q16_16 mapped to Int32. -/
def update (s : State) (v_t : Int32) : State :=
let v_q := _root_.Semantics.Q16_16.ofInt v_t.toInt
let phiNext := nextPhi s.phi
let theta_t := getThreshold phiNext
-- Step 3 & 4: Error Accumulation and Symbol Decision
let b_t := if theta_t < v_t + s.error then true else false
let e_next := v_t + s.error - (if b_t then theta_t else 0)
-- Step 5-8: Tension and Phase (Neutralized SLUQ)
let stress := (e_next).abs
let tensionNext := (s.tension * 921 + stress.toUInt32 * 103) / 1024
let phaseNext :=
if tensionNext > 50000 then Phase.seismic
else if tensionNext > 10000 then Phase.drift
else Phase.grounded
-- L5: Update bracket (Constraint-preserving interval)
let newBracket := BracketedDIAT.encode
(s.bracket.lower + v_q - _root_.Semantics.Q16_16.epsilon)
(v_q)
(s.bracket.upper + v_q + _root_.Semantics.Q16_16.epsilon)
s.bracket.scale
{ phi := phiNext
, error := e_next
, tension := tensionNext
, phase := phaseNext
, lastSymbol := b_t
, bracket := newBracket }
end State
end Semantics.PBACSSignal