{"id":"e-070da67d980ebd97","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-3cc7875cf81a5a84","premise_count":0,"theorem":"polytool parent provers, route periodic_product: every parent row P_n, n >= 1, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"4b057e66c28eed36143b9f176a2bc6d9c2e929e338c12f580ae6fc1b6b85ef5d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":630,"certificate_compressed_size":373,"conclusion_name":"basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shifted by x -> -x + 0","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-3cc7875cf81a5a84","claim":"real_rooted"},{"node_id":"n-3cc7875cf81a5a84","claim":"one_signed_coefficients"},{"node_id":"n-3cc7875cf81a5a84","claim":"hadamard_kernel"}]}