The dominant trajectory of contemporary artificial intelligence assumes that cognitive capability primarily arises from continuous scaling of computation, model parameters, data, and energy consumption. In this paper, we present a principled counterexample. We formally distinguish two classes of intelligence growth paradigms: Compute-Driven Intelligence (CDI) and Structure-Driven Intelligence (SDI). Under minimal physical and computational assumptions, we prove that, given a fixed long-term energy budget, CDI systems exhibit an intrinsic and non-surpassable upper bound on achievable capability, whereas SDI systems do not admit an equivalent bound. We further outline a coherent cognitive system architecture consistent with the SDI paradigm, grounded in identity persistence, action–feedback–cost causality, and the cumulative construction of structured concepts. This result demonstrates that equating intelligence progress with compute and energy scaling is theoretically incomplete, and that an alternative path exists toward long-term, energy-bounded, and historically accumulative intelligence.