Molecular property prediction is crucial for drug discovery when labeled data are scarce. This work presents CardinalGraphFormer, a graph transformer augmented with a query-conditioned cardinality-preserving attention (CPA) channel that retains dynamic support-size signals complementary to static centrality embeddings. The approach combines structured sparse attention with Graphormer-inspired biases (shortest-path distance, centrality, direct-bond features) and unified dual-objective self-supervised pretraining (masked reconstruction and contrastive alignment of augmented views). Evaluation on 11 public benchmarks spanning MoleculeNet, OGB, and TDC ADMET demonstrates consistent improvements over protocol-matched baselines under matched pretraining, optimization, and hyperparameter tuning. Rigorous ablations confirm CPA's contributions and rule out simple size shortcuts. Code and reproducibility artifacts are provided.