Statistical Structure and the Failure of Pointing: A System-Class Law for Compression-Based Generative Systems

This paper proposes a system-class law for large language models as compression-based generative systems: statistical structure is preserved under compression, whereas indexical structure — the recoverable relation between an output and its originating evidential context — is not preserved in its pointing function. The asymmetry between statistical structure and indexical structure is not a contingent deficiency of current models but a structural property of compression-based generation. Compression preserves recurring regularities across the training distribution, but it does not thereby preserve particular pointing relations as such. From this law follows the Grounding Ceiling: increases in predictive capability can improve calibration and surface accuracy but cannot by themselves make output generation constitutively evidential, because the generation process does not traverse the evidential relations grounding requires. A conditional extension of the law, the Control Ceiling, follows if future empirical work confirms that inference proceeds through stable behavioural regimes shaped by pretraining: post-training control methods cannot then be assumed to arbitrarily rewrite that underlying regime structure. Together, these two ceilings establish a methodological consequence: current evaluation practices are organised primarily around surface plausibility rather than around the deeper properties this account identifies as explanatorily fundamental — grounding recoverability at the compression level and stable regime structure at the dynamical level. Once the evaluative target shifts, capability forecasting, interpretability, safety, and design change in kind.