{"id":"e-ac757e303466262b","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-8cad05f13f2c85cb","premise_count":0,"theorem":"all-index identity Q_n = P_n certified by exact Ore-algebra division and identifying rows (polytool preserver-image certificate of the identity map)","lean_route":null,"lean_declarations":[],"certificate_hash":"be3b4471411d2cb89c34529251a52f89b0c863e27ddf2f1347bad5f443980e5c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":9001,"certificate_compressed_size":2590,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having genus k (see first comment for definition of genus).","claims":[],"premises":[],"cited_by":[]}