When the Square Touches the Circle Generalized Resonant Contact Across Scale A Structural Extension of Resonant Compatibility and Multidimensional Psychological Architecture

Resonant compatibility formalizes conditions under which two self-led psychological systems can couple without degrading internal coherence. However, compatibility-relevant contact is not limited to dyadic romantic relationships. Across creative, institutional, ideological, and cultural contexts, self-led systems repeatedly interface with external structures that either support circulation or induce depletion, capture, or collapse. This paper generalizes resonant compatibility into a scale-agnostic Circle–Square framework. The Circle denotes any self-led system that preserves internal authorship through a minimal recursive continuation loop (I am → I choose → I continue). The Square denotes any external structure capable of sustained interface with the Circle without assuming regulatory authority. Compatibility is defined structurally as preservation of authorship, exit capacity, and temporal renegotiability under contact. Sustained contact is modeled as requiring (1) resonance constraint alignment and (2) non-redundant secondary regulatory orientation at the interface. The framework differentiates conductive, resistive, amplifying, and distorting flow characteristics of Circle–Square contact. These flow characteristics describe relational dynamics rather than traits of persons or structures. The model specifies failure modes through which contact becomes destabilizing, including authority migration, exit penalty, identity fusion, and conditional continuation. The paper is descriptive and formulation-oriented. Permissions NoticeThis work is licensed under Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Any use involving adaptation, modification, translation, educational deployment, therapeutic application, derivative modeling, or inclusion in external platforms beyond unchanged archival hosting requires explicit written permission from the author.