{"id":"e-900563a8e48842d5","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-dfedc6a36c97eba4","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":"2fe6ebf99fd4ab575d8b9185f003c103b7118e2ba296ca2677f29dfa81ac3f16","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1588,"certificate_compressed_size":741,"conclusion_name":"Triangle read by rows: T(n, k) = t(n-k, k), where t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0, else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), and f(n) = 3*n + 3.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-dfedc6a36c97eba4","claim":"one_signed_coefficients"},{"node_id":"n-dfedc6a36c97eba4","claim":"hadamard_kernel"},{"node_id":"n-dfedc6a36c97eba4","claim":"real_rooted"}]}