The RRK‑7 Minimal Model: Recursive Dominance as a Universal Mechanism for Meta‑Structure Formation

This study introduces and analyzes the RRK‑7 Minimal Model, a formal and empirically testable core of the RRK‑7 theoretical framework. The model defines a recursive agent system governed by two parameters: self‑reference ( 𝛼 ) and recursive coupling ( 𝛽 ), with 𝛼 + 𝛽 = 1 . System coherence is operationalized as normalized variance reduction. RRK‑7 predicts that meta‑structures emerge when recursive coupling exceeds self‑reference ( 𝛽 > 0.5 ). We provide a mathematical analysis, numerical simulations, and a fully specified empirical experiment using LLM agents. Results show that systems with 𝛽 > 0.5 reliably cross the coherence threshold 𝜏 \* = 0.6 , forming stable meta‑structures. Systems with 𝛽 < 0.5 do not. This establishes RRK‑7 as a falsifiable and domain‑general hypothesis about emergent organization in recursive systems.