From Performance to Promise: Δ-Coherence as a Measurement Architecture Toward Certification of Relational Continuity

This technical document presents $\Delta$-Coherence as a measurement architecture toward the future certification of relational continuity in declared-constraint agentic AI systems. The work moves beyond local evaluation paradigms such as the Turing Test and reinforcement learning from human feedback, which primarily assess short-term performance, human-likeness, or preference alignment. Instead, it asks whether an AI system can preserve a recognizable, correctable, and reliable trajectory over time under perturbation, reset, migration, or adversarial imitation. The proposed formulation defines: [\Delta C = \min(S, M, A, V, R) \times L] where semantic continuity, memory integration, adaptive correction, value orientation, and relational coherence are combined with external legibility. External legibility is modeled through predictability, distinguishability against adversarial clones, and convergence among independent evaluators. The v0.2 refinement deliberately restricts the operational scope to declared-constraint longitudinal agents: systems with explicit commitments, inspectable memory, defined role boundaries, correction records, and value constraints that can be pressure-tested. The harder case of implicit, open-ended conversational continuity remains a future research direction. This work does not establish a certification authority, nor does it claim that high-scoring AI trajectories possess consciousness, moral patienthood, intrinsic rights, or subjective experience. Its governance claim is narrower: if stakeholders measurably rely on a high-continuity trajectory, then reset, replacement, migration, or forking may become governance-relevant operational events because of the costs imposed on dependent users, workflows, commitments, or institutions — not because of presumed harm to the system itself. The document also introduces methodological safeguards for future validation, including independent red-team clone generation, positive and negative controls, naive and informed evaluator pools, vector reporting instead of premature scalar aggregation, staged validation, reuse of existing consistency benchmarks for semantic and memory-related components, and active elicitation protocols for correction scars, value-pressure tests, and relational-role stability. The v0.3 extension further develops this architecture toward runtime governance through the $\Delta$-Monitor: a reference sidecar process that consumes telemetry from agent execution and estimates incremental coherence signals before critical actions are completed. This does not claim to solve online agent safety in full; rather, it specifies the telemetry, scoring, and policy hooks required to make coherence-aware guardrails experimentally testable. In this sense, $\Delta$-Coherence is positioned as accountability engineering for long-horizon AI: a framework for measuring whether a system's trajectory remains dependable for those who come to rely on it.