{"id":"e-5b61491b47fb76b5","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-f7935c36a3c0ec8c","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":"6d26f1876f659a40c2cffb1bd9a3f1399bc66b9c7ba39e664d9228e929dd3c3c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":14715,"certificate_compressed_size":3410,"conclusion_name":"Triangle read by rows: T(n, k) = binomial(2n, 2k).","claims":[],"premises":[],"cited_by":[]}