Scale-Free Structures

ABSTRACT: This paper builds on prior work proposing that DSRP (Distinctions, Systems, Relationships, Perspectives) names a minimal set of organizing roles shared by cognition and reality (𝕄 = I·O; ℝ = I·O) [1–6] . If the same eight elemental roles constrain both mental models and the world, then finding the same structural grammar across disciplines is not coincidence—it is a consequence of constraint. We test a falsifiable implication of this view: that explanations which achieve closure about a phenomenon will consistently externalize the full set of elemental roles and show non-trivial co-implication among them, whereas non-explanatory controls will not. Using fixed excerpts from multiple disciplines, plus narrative and raw-data controls, we apply a conservative, rule-based coding protocol to quantify elemental role coverage, Structural Co-Implication Index (SCI), and recursion indicators; robustness is assessed by independently executing the identical protocol on a second LLM. Results show that explanatory discourse reliably exhibits high role coverage and high co-implication relative to controls, consistent with a principle of Structural Confinement: when one tries to isolate structural roles, structure re-emerges because explanatory closure requires co-implicated organization. We do not claim DSRP is the “material” of reality; rather, it names closure constraints and structural roles that coherent systems and coherent explanations must satisfy. On this view, improved understanding comes less from accumulating content alone and more from correcting default structural bias so that the organization of mental models increasingly aligns with the organization of their targets (𝕄/ℝ).