{"id":"e-6aae761843f53e9e","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-b8c7876a249ffefc","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":"76324276a28719d3e6ea68d76afcf3f6c71411df5e4d0e70939d919dca8cea38","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":10608,"certificate_compressed_size":2950,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n,k) is the number of flattened Catalan words of length n with exactly k runs of descents.","claims":[],"premises":[],"cited_by":[]}