BU36 B_U as Complex-System Unified Settlement Axiom From Organizational Clearing to Historical Cycles and Stage Identification

This paper extends B_U from a physical closure theory into a complex-system unified settlement axiom. Its central chain—background clearing, admissible carrier, directional amplification, unified settlement, and resolution ascent—maps stable operation across organizations, economies, accounting systems, audits, governance structures, and civilizational cycles. The note argues that durable systems must first clear bottom-level residuals, debts, frictions, and noise before they can form legitimate carriers, amplify direction, return growth and risk to one ledger, and move toward higher resolution. The framework then distinguishes real carrier from possession drift, amplification from narrative drift, and residual pressure from retained-chain expectation. It treats debt, bad accounts, and unclosed obligations as residual structures, while stock indices appear as market-compressed projections of future retained-chain strength. Resolution ascent is defined as a costly upgrade of governance precision, organizational complexity, technical capacity, and decision resolution. At the civilizational scale, historical cycles are reclassified as periodic returns of unified settlement constraints: flourishing periods reflect stable carrier, effective amplification, and unified settlement, while chaotic periods expose rising background debt, loose carrier, runaway amplification, and settlement distortion. The final methodological claim is that complex-system governance begins with stage identification: once the system’s stage is located, its primary contradiction and optimal direction become visible.