{"id":"e-0050d566ad712b7d","operation":{"operation":"parent_provers","route":"paper_theorem"},"operation_detail":"paper_theorem","conclusion_id":"n-e189038e95d51606","premise_count":0,"theorem":"polytool parent provers, route paper_theorem: every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"9512eddffa6eb79b68454c8f9d408750984a9487d8198b7dd9368d8d151b56c8","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":2276,"certificate_compressed_size":967,"conclusion_name":"Triangle T(n,k) = T(n-1,k) + 3*T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1, T(n,k) = 0 for n or k < 0, read by rows.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-e189038e95d51606","claim":"real_rooted"},{"node_id":"n-e189038e95d51606","claim":"one_signed_coefficients"},{"node_id":"n-e189038e95d51606","claim":"hadamard_kernel"},{"node_id":"n-e189038e95d51606","claim":"interlacing"}]}