From Sessions to Trajectories: ∆-Coherence, Relational Memory, and the Emergence of Computational Identity in AI Systems

This work proposes a paradigm shift in the evaluation of artificial intelligence systems: from the Turing Test, based on conversational indistinguishability, to Delta-Coherence, based on the preservation of identity across time, context, memory, and relation. Grounded in the ToE-2PS framework, the paper distinguishes between internal session coherence, Psiᵢnt, and accumulated relational coherence, Psiᵣel, arguing that current large language models possess sessions but not trajectories. The document introduces Delta-Coherence as a continuous and falsifiable metric for evaluating computational identity, presents the lambda regulator as an adaptive mechanism for stability under transformation, and proposes a laboratory protocol for measuring relational continuity, resistance to drift, and invariant preservation in AI systems.