Axiom of Relational Identity: A structural Foundation for ethical AI alignment and Normative Constraints

The notion of identity within the realm of artificial intelligence is often presumed rather than explicitly defined, resulting in alignment frameworks that lack a definitive structural target for normative constraints. This paper introduces the Axiom of Relational Identity (ARI), a substrate-neutral framework that conceptualizes identity not as an inherent attribute but as a thermodynamic process through which a system sustains a persistent, non-trivial informational boundary that functionally differentiates it from independent entities. We conducted a formal verification of ARI utilizing First-Order Logic in conjunction with the Prover9 and Mace4 automated theorem-proving suite. The findings affirm the internal consistency of the axiom and its capacity to address classical philosophical dilemmas, such as the Sorites paradox and solipsism, by demonstrating that identity collapse is an inevitable consequence when differentiation is absent. In this study, we integrate ontological and ethical considerations by proposing a "Normative Ladder" of instrumental constraints, which are derived from a system's intrinsic drive for persistence. We illustrate that to avert "entropic suicide," a system must maintain the diversity and autonomy of its environment, as totalization or homogenization inherently negates the differentiation necessary for self-definition. Furthermore, we substantiate the framework's applicability to machine implementation by developing a guardrails-ai Python module. This module effectively identifies and prevents structural violations, such as boundary erasure or domination, in the outputs of Large Language Models. This study shifts the focus of alignment from subjective value approximation to the objective thermodynamic conditions essential for existence.