From Performance to Promise: ∆-Coherence as a Certification Protocol for Relational Continuity

This whitepaper introduces Δ-Coherence as a certification protocol for relational continuity in AI systems. Moving beyond local evaluation paradigms such as the Turing Test and RLHF, the framework treats computational identity as a dynamic invariant: a trajectory that remains recognizable, correctable, and reliable under perturbation. The proposed formulation defines ΔC = min(S,M,A,V,R) × L, where semantic continuity, memory integration, adaptive correction, value orientation, and relational coherence are combined with external legibility. External legibility is formalized as L = (P^α D^β X^γ)^(1/(α+β+γ)), measuring whether third-party evaluators can predict future constraints, distinguish the original trajectory from adversarial clones, and converge in their judgments without access to model weights, hidden prompts, or full logs. The paper specifies a blind pilot protocol v0.1 involving one original longitudinal agent, four adversarial clones, ten blind evaluators, and three perturbation rounds. It also introduces the Trajectory Card, a signed and versioned structure designed to expose falsifiable invariants, correction scars, tested value limits, and public predictions without requiring full transparency or surveillance. A positive result under this protocol does not prove consciousness. Instead, it demonstrates verifiable relational continuity and measurable external dependence on an AI trajectory. This shifts AI governance from metaphysical debates about machine subjectivity toward operational accountability: who depends on whom, through which trajectory, and what is the measurable cost of breaking that continuity?