Formalizing Scar Structure and the Closure Condition
Zenodo (CERN European Organization for Nuclear Research) May 30, 2026 Samuel Richards
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.