Resource-Bound Democracy Ceiling Mathematical Model
Resource-Bound Democracy Ceiling Model 1. System State Definition The macro-economic environment is represented as a dynamic state vector: π(π‘)=⟨π
(π‘),π(π‘),ΞΌ(π‘),πΊ(π‘),πΊπ·Pπ(π‘),π(π‘)⟩ Where: (π
(π‘)) = total national resources / wealth index (π(π‘)) = population (ΞΌ(π‘)=π
(π‘)/π(π‘)) = mean per-capita wealth (πΊ(π‘)) = inequality index, (0 ≤ πΊ ≤ 1) (πΊπ·Pπ(π‘)) = GDP growth rate (normalized) (π(π‘)) = social-stress index (unemployment, wage-gap, housing) Commentary: The system evolves continuously in time. The wealth ceiling must remain consistent with macro-state changes. 2. Boundary Logic — Democratic Stability Conditions Tyranny suppression condition: lim₍G(t) → 1₎ Wβββ(t) = 0 Equality stability condition: lim₍G(t) → 0₎ Wβββ(t) = k(t) · ΞΌ(t) Continuity requirement: Wβββ(t) ∈ C¹(β⁺) Commentary: The model guarantees tightening at extreme inequality and relaxation in equitable states, without discontinuities or shocks. 3. Base Wealth Ceiling Function Wβββ(t) = k(t) · ΞΌ(t)...