{"id":"e-a32213ca02c6584d","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-69c5ad82a7bc1667","premise_count":2,"theorem":"Hermite--Kakeya--Obreschkoff: real-rooted f, g with interlacing zeros give a zero or real-rooted a f + b g for all real a, b (Obreschkoff 1963; Fisk, Polynomials, roots, and interlacing, Thm 1.43)","lean_route":null,"lean_declarations":[],"certificate_hash":"3128b8770f9c4d30a73efdd052372a26734cd4b8198cb90df0fc55635417136d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":12996,"certificate_compressed_size":2894,"conclusion_name":"obreschkoff_combination of Triangular array A066667 or A008297 unsigned and transposed.","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-d55979c30b97975a","role":"sequence","name":"Triangular array A066667 or A008297 unsigned and transposed.","uses":{"claim":"real_rooted","from_index":0,"region":{}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)"},{"position":1,"node_id":"n-d55979c30b97975a","role":"sequence","name":"Triangular array A066667 or A008297 unsigned and transposed.","uses":{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"},"uses_text":"Rows P_(m-1), P_m interlace (weak, unordered) for every m >= 1"}],"cited_by":[{"node_id":"n-69c5ad82a7bc1667","claim":"real_rooted"}]}