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debe354 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | -- MetaSum.lean (QuantumAP)
-- Formal definition of MetaSum and Sovereign Shift for the Quantum AP Orchestrator
-- Source: Ahmad Ali Parr 2026-08-16
--
-- θ = 89/2462: the closed loop parameter
-- MetaSum = phase-weighted direct sum on NC Torus T²_θ
-- Dream Cycle = self-healing phase crystallization
import Mathlib.Analysis.SpecialFunctions.Log.Basic
open Real
-- Sovereign Shift
def sovereignShiftNum : ℕ := 89
def sovereignShiftDen : ℕ := 2462
theorem sovereign_shift_coprime : Nat.Coprime sovereignShiftNum sovereignShiftDen := by
native_decide
theorem sovereignShiftNum_prime : Nat.Prime sovereignShiftNum := by
native_decide
-- Period: V^2462 commutes with U
theorem lateral_period : sovereignShiftDen = 2462 := rfl
-- Winding: 89 full phase rotations per cycle
theorem phase_winding : sovereignShiftNum = 89 := rfl
-- The Weyl relation structure
structure NCTorus where
q : ℕ -- dimension (= 2462)
p : ℕ -- winding (= 89)
coprime : Nat.Coprime p q
-- MetaSum validity condition: entropy ≤ 0.20
structure MetaSumValid where
magnitude : ℝ
entropy : ℝ
mag_positive : magnitude > 0
entropy_bounded : entropy ≤ 0.20
-- Dream Cycle: triggered when magnitude < threshold
structure DreamCycleResult where
recovered_magnitude : ℝ
recovery_achieved : recovered_magnitude > 512 -- N/2
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