{"id":"e-363ec3019ccc29a9","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-7c641d81e21514ce","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":"bc953de90d6126a0fb424adc5d8633e01177fe6b5f347a33523da03b2357bb7d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":635,"certificate_compressed_size":382,"conclusion_name":"Triangle read by rows: T(n,k) is the number of ternary words of length n having degree of asymmetry equal to k (n>=0; 0<=k<=n/2).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-7c641d81e21514ce","claim":"real_rooted"},{"node_id":"n-7c641d81e21514ce","claim":"one_signed_coefficients"},{"node_id":"n-7c641d81e21514ce","claim":"hadamard_kernel"}]}