Hierarchical bounds on RNA chromatin statistical dependence across cellular states in paired single-cell multiome data

Understanding how transcriptional output and chromatin accessibility coordinate across cellular states remains a central challenge in multimodal single-cell biology. Here, we establish explicit hierarchical empirical bounds on RNA-chromatin statistical dependence using a strictly falsification-driven, information-theoretic analysis of paired RNA-seq and ATAC-seq data. Our contribution is not to assert universal coupling, but to quantify the maximum intra-state coupling that survives adversarial nulls, thereby converting qualitative intuition into empirical bounds. Leveraging unimodal latent representations and adversarial null models, we quantify both the existence and the limits of cross-modal dependence across organizational scales. At the population level, global RNA-ATAC mutual information is strong and reproducible across donors, but is shown to be overwhelmingly dominated by cell-type composition rather than fine-grained regulatory coordination. When cellular state is explicitly controlled, intra-state RNA-ATAC coupling collapses to null expectations in the majority of populations, directly falsifying the hypothesis of a universal within-state regulatory channel. Despite this collapse, a weak but statistically robust residual coupling persists in a restricted subset of highly dynamic states, including erythroid differentiation compartments, activated T cells, and NK cells. This residual signal survives stringent local permutation tests and conditional mutual information analysis, demonstrating that it cannot be reduced to compositional mixing alone. Quantitatively, residual within-state dependence is consistently an order of magnitude smaller than global dependence, placing an empirical upper bound on within-state RNA-ATAC coordination in this dataset. Donor-resolved ratios {rho} = I(R;A|S)/I(R;A) indicate that most of the global dependence is removed by conditioning on state; operationally, we refer to the removed fraction (1-{rho}) as composition-dominated dependence. Throughout, "state-contingent statistical dependence" is used strictly as an operational descriptor rather than a causal claim: mutual information and conditional mutual information quantify statistical dependence only, not directionality or mechanism. This framing constrains downstream mechanistic interpretation and future multimodal modeling.