Tabular foundation models (TFMs) pretrain a transformer on large-scale synthetic priors so that a single forward pass yields zero-shot tabular prediction. TabICLv2 samples the class count of its classification prior during pretraining, and the prevailing configuration caps it at ten. We report a counter-intuitive result: setting this cap directly to two---making every pretrained classification task binary---still yields weights that perform zero-shot K-way classification 2. On the 38 TabArena classification datasets (200 bootstrap rounds, anchored at default RF = 1000), the binary two-stage recipe reaches 1590.1 Elo, above the official default at 1568.0 (+22.1), above TabPFN-v2.6 (1577.1) and RealTabPFN-v2.5 (1521.6). A production-scale validation on 60 real-world credit-scoring institutions independently confirms the direction: the same checkpoint improves test AUC on 44 of 60 institutions (paired Wilcoxon p = 0.0007 for AUC, p = 0.0002 for KS) at +1.5 inference cost. Mechanistically, classification in TabICLv2 is carried not by a fixed-cardinality output head but by an in-context comparison operator matching query-row embeddings against class-conditional embeddings, so the cardinality of the output space is set by the labels present in the context, not by the label space seen during pretraining. This makes a binary prior structurally cheaper to generate and cache than a ten-class prior, demotes "number of classes" from an architectural constraint to a tunable hyperparameter, and points to a class-count-agnostic regime of TFM pretraining.

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