{"id":"e-7d57ae2f42078672","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-9f6ff7cc417b165f","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":"9d4d9d2298e2533d0d0e1ec385de02e4019287ffc7cf547c680dfbbc6507f11c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":6374,"certificate_compressed_size":1575,"conclusion_name":"obreschkoff_combination of Coefficient array of Hermite_H(n, (x-1)/sqrt(2))/(sqrt(2))^n.","claims":[{"claim":"real_rooted","from_index":1,"region":{}}],"premises":[{"position":0,"node_id":"n-f0c4b6406e0da4a3","role":"sequence","name":"Coefficient array of Hermite_H(n, (x-1)/sqrt(2))/(sqrt(2))^n.","uses":{"claim":"real_rooted","from_index":1,"region":{}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, +inf)"},{"position":1,"node_id":"n-f0c4b6406e0da4a3","role":"sequence","name":"Coefficient array of Hermite_H(n, (x-1)/sqrt(2))/(sqrt(2))^n.","uses":{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"},"uses_text":"Rows P_(m-1), P_m interlace (weak, unordered) for every m >= 2"}],"cited_by":[{"node_id":"n-9f6ff7cc417b165f","claim":"real_rooted"}]}