Probing transformer reasoning transfer through alphabet equivalence

A reasoner is abstract if it applies a general procedure to a problem's structure, indifferent to how that structure is concretely instantiated; it is concrete if what it learned is tied to the particular instantiation trained on. This gives a testable marker: an abstract reasoner should transfer mastery of one problem instance to another. We study equivalence via alphabet renaming, and test transfer using a weight-transplant control – copying trained per-symbol weights onto the new instance without retraining – distinguishing genuine reasoning failure from symbols never trained on. We instantiate this with Sudoku, where an equivalent puzzle is any relabeling of its digits. A transformer trained on one such puzzle transfers to an equivalent one no better than an untrained network – yet the transplant control recovers its original performance exactly. Reasoning, in that narrow sense, is abstract; recognizing that a new instance calls for it is not. We probe this recognition gap three ways. Freezing the shared network and adapting only a new alphabet's parameters fares worse than training an unfrozen model from scratch on the same data: prior exposure to other alphabets does not ease learning a new one. Recombining already-known symbols into unfamiliar combinations yields graded, partial success – above chance, short of the seamless transfer an abstract reasoner should show, degrading as combinations diverge from training. Replacing the model's fixed, per-alphabet output vocabulary with a mechanism that selects among a puzzle's own visible symbols helps substantially with recombination, but only marginally with transfer to a truly unseen alphabet. These results isolate a specific failure to recognize alphabet-equivalent instances as such, distinct from a general failure to reason, and show several natural interventions narrow, but do not close, this gap.