Structuring Forces and Systemic Thresholds: A Unified Law of Emergence across Scales

This paper presents a formal articulation of the Law of Structuring Systemic Emergence (LESSE), the central theorem of the Systemic Continuum Paradigm (SCP). It posits that at each scale of organization, only one dynamic can monopolize the General Systemic Balance (GSB)—the emergent synergy that defines that level—by crossing a Systemic Threshold (ST) derived from internal interactions (ISB). All other properties, while present, remain subordinate. The LESSE provides a transdisciplinary framework for understanding how structuring forces such as gravity, intelligence, metabolism, or governance emerge as dominant only when their systems surpass the synergy required for ontological ignition. This threshold logic applies not only to physical systems, but also to biological, social, technological, and cognitive architectures. The paper introduces algebraic scaffolds for key metrics—including the Systemic Dominance Index (SDI) and Integrated Co-evolutionary Synergy (ICS)—and offers eight multiscale case studies, from single-celled organisms to neural architectures and planetary economies. Unlike unification models that search for foundational particles or final equations, the SCP identifies emergence as a scale-bound monopoly: a law of hierarchical resonance rather than universal identity. This formulation marks the fifth installment in the SCP corpus, and constitutes its first rigorous formalization—designed to support future mathematical development, empirical testing, and cross-domain application.