{"id":"e-5a4f04ff49b735c1","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-477d9807e1cbb785","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":"7527db23ea6625be2e5717d38ea1b157002ee3f03442de5605617ff06d746112","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":630,"certificate_compressed_size":374,"conclusion_name":"basis-map coefficients of Triangle read by rows: T(n,k) = binomial(k,n-k). shifted by x -> -x + 0","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-477d9807e1cbb785","claim":"real_rooted"},{"node_id":"n-477d9807e1cbb785","claim":"one_signed_coefficients"},{"node_id":"n-477d9807e1cbb785","claim":"hadamard_kernel"}]}