Informational Linkage Gaps and the Structural Limits

We apply the informational linkage gap framework (Montanino 2026a) to the scaling hypothesis in large language models (LLMs), formulating a structural claim about the limits of compute-based improvement. The framework identifies three classes of discrimination barriers: energetic (C_E), computational (C_C), and navigational (C_nav). The scaling hypothesis — that increasing compute and training data monotonically improves AI capabilities — is sound for Barrier I problems (C_E, C_C): problems where a solution procedure exists within the training distribution and more compute reduces error. It fails structurally for Barrier IIb and III problems: problems requiring cross-domain connective concepts c* whose Kolmogorov complexity K(c*) exceeds what interpolation over the training distribution can represent. We formulate this as the LLM Ceiling claim: for any problem P requiring a connective concept c* with K(c*) > K_max(D), where D is the training distribution, no amount of scaling within D produces a system that solves P above the base rate of task-correct outputs among surface-plausible responses. The ceiling K_max(D) is a property of the training distribution, not of model size. We derive three falsifiable predictions distinguishing Barrier I from Barrier IIb/III problems in LLM benchmarks, and discuss implications for AI alignment: alignment problems that require genuine cross-domain concept construction — not pattern matching — may lie outside the scaling regime. Keywords: informational linkage gaps · scaling laws · large language models · Kolmogorov complexity · cross-domain generalization · AI safety · AI alignment · computational epistemology · connective concepts · Barrier IIb · test-time compute