{"id":"e-bf1e7898c429e3eb","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-cb5d49e71e46f2ed","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":"53e3e2f50c68473853bbad3202c714de4297b3debd814b496619ff6c6f7a660a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1158,"certificate_compressed_size":606,"conclusion_name":"Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-cb5d49e71e46f2ed","claim":"one_signed_coefficients"},{"node_id":"n-cb5d49e71e46f2ed","claim":"hadamard_kernel"},{"node_id":"n-cb5d49e71e46f2ed","claim":"real_rooted"}]}