{"id":"e-f2db3ed118a27f94","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-41809911e05bb4ba","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":"222cc595d078b61fc1f4a51a0239270326ba2244b1e4968cf2fcb43a70ed6aea","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1453,"certificate_compressed_size":703,"conclusion_name":"Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 2*x + 2.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-41809911e05bb4ba","claim":"one_signed_coefficients"},{"node_id":"n-41809911e05bb4ba","claim":"hadamard_kernel"},{"node_id":"n-41809911e05bb4ba","claim":"real_rooted"}]}