{"id":"e-f329640d21a7ba5a","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-60c7e36cbe887b7e","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":"7f1f5f48a2813356605e4c28e2b09dabc8b3dee6606770d46402dcd9a8ed61e2","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1406,"certificate_compressed_size":706,"conclusion_name":"Coefficients of raising factorial polynomials, T(n,k) = [x^k] p(x, n) where p(x, n) = (m*x + n - 1)*p(x, n - 1) with p[x, 0] = 1, p[x, -1] = 0, p[x, 1] = m*x and m = 2. Triangle read by rows, for n >= 0 and 0 <= k <= n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-60c7e36cbe887b7e","claim":"real_rooted"},{"node_id":"n-60c7e36cbe887b7e","claim":"one_signed_coefficients"},{"node_id":"n-60c7e36cbe887b7e","claim":"hadamard_kernel"}]}