{"id":"e-088407700c450d53","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-c7809537965f400d","premise_count":0,"theorem":"polytool parent provers, route root_domain: every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"e58ce5d9f614f6f9e624a67dfff362ff70d62394601b24ec342355a8dcd8c3d2","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1160,"certificate_compressed_size":609,"conclusion_name":"Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-c7809537965f400d","claim":"one_signed_coefficients"},{"node_id":"n-c7809537965f400d","claim":"hadamard_kernel"},{"node_id":"n-c7809537965f400d","claim":"real_rooted"}]}