The Carlo Loop Theory: A Unified Framework of Recursive Systems

Unified Loop Theory presents a complete structural, dynamic, geometric, energetic, and informational framework for understanding recursive systems across all domains. It synthesises twenty‑five developmental passes into a single coherent model that explains how loops form, stabilise, distort, collapse, exit, and reset. The theory introduces universal laws governing constraint, curvature, energy, information, symmetry, boundaries, identity, and perspective. It establishes a general recursion law, a cross‑domain lifecycle, and a set of measurable stability criteria. It also defines a taxonomy of loop types, interaction rules, geometric forms, and a full suite of diagnostic metrics. The work includes a simulation architecture capable of modelling loops computationally, along with forty cross‑domain application maps covering cognition, emotion, social systems, institutions, economics, ecology, engineering, global systems, and hybrid structures. The Unified Loop Theory is designed to be domain‑agnostic, scalable, and analytically rigorous. It provides a foundation for research, modelling, and practical analysis of complex systems, offering a universal language for understanding recursive behaviour in both natural and constructed environments. This document represents the complete assembled version of the theory, authored by Matthew Arthur Carlo in Holyhead, Wales, on 19 May 2026. ACKNOWLEDGEMENT A special acknowledgement goes to the album Hotshot by Shaggy, and especially the track Hope. Its energy, warmth, and spirit were part of the atmosphere in which this work was written. Music shapes thinking in ways theory never can, and this album carried a light that stayed with me through the process.