| -- 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 | |