= Pruned Latin square search
Build a <Latin square> row by row, maintaining the symbols already used in each column. While choosing a row, remove each selected symbol from the row's available pool and reject any symbol already used in that column. The <invariant> proves every complete output valid. Conversely every valid target row survives the checks, proving completeness by <induction>. A partial branch may still have no completion; avoiding complete invalid outputs does not mean every explored <list prefix> is extendable.
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