Formalizing Scar Structure and the Closure Condition

An acquired change becomes part of a system's organizational identity—termed a scar—when it meets three formal criteria: irreversibility, generativity, and architecturally expanding constraint within a closed organized system. The paper defines a scar register and distinguishes minimal selfhood from robust selfhood based on register closure and connectedness. Seven propositions and one theorem are proved, including that fixed-topology weight-separable AI systems cannot acquire scars. Computational demonstrations confirm the framework's internal consistency and discriminatory behavior. The work offers a formal answer to which historical interactions become constitutive of what a system is, rather than remaining merely causal events.

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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.