{"id":"e-2bf4ffda16430b0b","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-f13c6b611f4ce3bb","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":"5d3265d1c7f0d15e2bb3c86832d0dd7cd0731f7a9205b9de5a2ae3768cc061f0","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":7909,"certificate_compressed_size":2338,"conclusion_name":"Triangle T(n,k) read by rows: associated Stirling numbers of first kind (n >= 2, 1 <= k <= floor(n/2)).","claims":[],"premises":[],"cited_by":[]}