What You Pretrain On Matters: Synthetic Task Distributions Determine Tabular Foundation Model Quality

Tabular foundation models acquire their inductive biases almost entirely from synthetic pretraining distributions, yet prior design remains poorly understood. Standard synthetic priors are too well-behaved: they omit the confounding, structured missingness, distributional shift, and spurious support-query correlations that characterize real tabular data. We introduce O'Prior, a compositional realism prior built around four coupled components: a hierarchical SCM meta-generator spanning diverse functional families; a modular realism engine covering heterogeneous marginals, missingness, and target transforms; an explicit stress module injecting confounding and support-query mismatch; and a curriculum-governed, leakage-safe generation protocol. Holding architecture, optimizer, and compute budget fixed, O'Prior yields consistent and substantial improvements across real tabular benchmarks. Ablations confirm that mechanism diversity, realism composition, and shift-aware stress each contribute independently, establishing synthetic prior construction as a first-order and largely overlooked determinant of tabular foundation model quality.