{"id":"e-9aedabfb67a4638b","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-344e4bfa9933088a","premise_count":0,"theorem":"polytool parent provers, route periodic_product: every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"de62cf87186a47e564cc50db07434793ff739f508b33e2df57374ff7ee78b2f3","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":645,"certificate_compressed_size":387,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*11^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-344e4bfa9933088a","claim":"one_signed_coefficients"},{"node_id":"n-344e4bfa9933088a","claim":"hadamard_kernel"},{"node_id":"n-344e4bfa9933088a","claim":"real_rooted"}]}