{"id":"e-e1335508951e1bb9","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-fac4d4a000d744e8","premise_count":0,"theorem":"L. L. Liu and Y. Wang, Adv. Appl. Math. 38 (2007) 542-560, Theorem 2.1 and Corollary 2.4 (A unified approach to polynomial sequences with only real zeros; the lag row as the interlacer, b_n = 0), weak interlacing of consecutive rows, with nonnegativity of the coefficients replaced, where a root region is certified, by an exact root-location induction; Proposition 3.3 (the case B_n(x) = -(c_n x + d_n)^2)","lean_route":"sign","lean_declarations":["RealRooted.threeTerm_interlaces_of_eval_nonpos","RealRooted.threeTerm_interlaces","RealRooted.eval_nonpos_of_natDegree_le_two"],"certificate_hash":"eff27b49fcd0b5bb280739ad3117118cc16d79f0573d1a31b7d70613aaf4949c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":4763,"certificate_compressed_size":1519,"conclusion_name":"Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":false,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-fac4d4a000d744e8","claim":"one_signed_coefficients"},{"node_id":"n-fac4d4a000d744e8","claim":"hadamard_kernel"},{"node_id":"n-fac4d4a000d744e8","claim":"real_rooted"},{"node_id":"n-fac4d4a000d744e8","claim":"interlacing"}]}
