{"id":"e-3e9b67ef5f31843c","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-51b4f5e7901c2b50","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":"2345c5ddbe100ef22613b342bb963e8952e7944989fa975723ead858fa14d9db","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":629,"certificate_compressed_size":375,"conclusion_name":"Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n >= 1, 0 <= k <= n-1). A level is a pair of identical consecutive letters.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-51b4f5e7901c2b50","claim":"one_signed_coefficients"},{"node_id":"n-51b4f5e7901c2b50","claim":"hadamard_kernel"},{"node_id":"n-51b4f5e7901c2b50","claim":"real_rooted"}]}