{"id":"e-aa6a1f197b91b3b6","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-1a0f876fa1441737","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":"b7c12a3b9ae25a3e4d7981f9e3d38ff781f8d0f558a8fde84bfbc63dfe4e014d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1159,"certificate_compressed_size":608,"conclusion_name":"basis-map coefficients of Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)} and m = 3. shifted by x ->  x + 1","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-1a0f876fa1441737","claim":"real_rooted"},{"node_id":"n-1a0f876fa1441737","claim":"one_signed_coefficients"},{"node_id":"n-1a0f876fa1441737","claim":"hadamard_kernel"}]}