theorem transition_iff_det_sign (e : SettlementEconomy) :
0 < e.self_phi * e.self_S - e.cross_phi_S * e.cross_S_phi ↔
settlementR0 e < 1 := by
simp only [settlementR0]
rw [div_lt_one (mul_pos e.h_self_phi e.h_self_S)]
constructor
· intro h; linarith
· intro h; linarithPaper 7: Settlement Feedback and Monetary Policy in a Mesh Economy