{"id":"e-ec342219c505666e","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-2255c682502f6ca3","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":"f1525e8a8f0c9c877ef424f44c46424c16324c18129a78cbbc926dc3ff97ae20","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1596,"certificate_compressed_size":742,"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+8*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-2255c682502f6ca3","claim":"one_signed_coefficients"},{"node_id":"n-2255c682502f6ca3","claim":"hadamard_kernel"},{"node_id":"n-2255c682502f6ca3","claim":"real_rooted"}]}