Formalizing Scar Structure and the Closure Condition

Abstract

This paper develops a formal framework for identifying when an acquired change becomes part of a system’s organizational identity rather than merely part of its causal history. Building on research in organizational closure, enactivism, and philosophy of biology, the paper introduces a computationally explicit account of scar structure: irreversible, generative, and architecturally expanding constraints acquired within a closed organized system. The framework defines three formal criteria for scar status, develops the concept of a scar register, and distinguishes minimal selfhood from robust selfhood through conditions of register closure and connectedness. The paper proves seven propositions and one theorem, including formal results concerning criterion separation, dissociation, organizational integration, and the conditions under which fixed-topology weight-separable AI systems cannot acquire scars. A suite of computational demonstrations validates the internal consistency, tractability, and discriminatory behavior of the framework. More broadly, the work addresses a central question in philosophy of biology and cognitive science: Which aspects of a system’s history become constitutive of what the system is? The proposed framework offers one formal answer by specifying when historical interactions generate organizationally significant constraints rather than remaining merely historical events. Relevant fields include philosophy of biology, theoretical biology, complex systems, enactivism, organizational closure, cognitive science, artificial intelligence, and theories of selfhood.