There Is a 13-Clue Suirodoku

A Suirodoku is an order-9 Graeco-Latin square in which each component satisfies the 3×3 block constraint of Sudoku. We show that the back-circulant alone admits 3,622,317,453 orthogonal mates, revealing 740 structural orbits and 734 species — a fusion rate of 0.8% under paratopism. The Sudoku-162 reveals an opposite regime: 1,129 orbits merge into 142 species (87.4% fusion). At the top of the hierarchy sits the Crystal Grid (1,296 symmetries), and the Sudoku-162 produces a stabilizer of order 81 — forbidden in classical Sudoku. On the minimum number of clues: classical Sudoku requires 17 (McGuire et al., 2014); for Suirodoku, 13 suffice. Full source code: https://github.com/teliance23/suirodoku-lab