{"id":"e-400776ae4466efdf","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-5cf6acfdac607d6d","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":"4f811f4d37a8fdc447c8452a9140a8177fbdbc0e6d7656dc2f0f51aeefeea17e","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":643,"certificate_compressed_size":387,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*7^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-5cf6acfdac607d6d","claim":"one_signed_coefficients"},{"node_id":"n-5cf6acfdac607d6d","claim":"hadamard_kernel"},{"node_id":"n-5cf6acfdac607d6d","claim":"real_rooted"}]}