{"id":"e-2dcf274e8e5380c5","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-f485cd65a8f8089f","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":"56ffb19deb5c3aea178b8b8da0e01858fb264286d0314c47e2fcaf924ea4a585","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":630,"certificate_compressed_size":376,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*9^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-f485cd65a8f8089f","claim":"one_signed_coefficients"},{"node_id":"n-f485cd65a8f8089f","claim":"hadamard_kernel"},{"node_id":"n-f485cd65a8f8089f","claim":"real_rooted"}]}