{"id":"e-67141f61fcf69367","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-6a8ffbe72ba42678","premise_count":0,"theorem":"polytool parent provers, route root_domain: every parent row P_n, n >= 1, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"41d3e65064450a3ab32c0e1727da89b86c6031853132a70aa03fbad2a54f1328","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1597,"certificate_compressed_size":739,"conclusion_name":"Triangle T(n, k) = coefficients of ( t(n, x) ) where t(n, x) = (1-x)^(n+1)*p(n, x)/x, p(n, x) = x*D( p(n-1, x) ), with p(1, x) = x/(1-x)^2, p(2, x) = x*(1+x)/(1-x)^3, and p(3, x) = x*(1+10*x+x^2)/(1-x)^4, read by rows.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-6a8ffbe72ba42678","claim":"one_signed_coefficients"},{"node_id":"n-6a8ffbe72ba42678","claim":"hadamard_kernel"},{"node_id":"n-6a8ffbe72ba42678","claim":"real_rooted"}]}