Toward a Complete Definition of AI Alignment: Functional-State Spaces, Adaptive Functions, and Generalised Semantic Back-Propagation

Most discussions of AI alignment rest on informal desiderata or on finite axiom sets that break down when optimisation pressure exploits their blind spots. Building on the Functional Model of Intelligence (FMI) and the Alignment Escape Velocity Theorem (AEVT), this paper argues that a complete definition of alignment must be grounded in the closed set of functions that make adaptation possible. Those functions—storage, recall, semantic modelling, recursive self-correction, compositional insertability, domain-general adaptivity, and bounded resource rationality—are jointly necessary and sufficient for sustained, reliable problem-solving and alignment in open environments. We embed these functions in a joint functional state space that spans body, emotion, conceptual cognition, and awareness for every human in the relevant group, and we show how generalised semantic back-propagation through a stochastic computation graph (SCG) supplies an unbiased credit-assignment mechanism that yields a unique ordering over policies. Although several quantitative sub-components remain to be empirically calibrated, every alignment proposal that omits them is formally vulnerable to Goodhart drift and recursive misalignment.