{"id":"e-a691d30fc1b4b246","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-a65976744dde69f6","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":"4fc3f3810a2eebd722eddc81f23e694422af434fd5e4b48f79c22e1ea811a90f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":11387,"certificate_compressed_size":2557,"conclusion_name":"obreschkoff_combination of Triangle of B-analogs of Stirling numbers of the second kind.","claims":[{"claim":"real_rooted","from_index":1,"region":{}}],"premises":[{"position":0,"node_id":"n-d55b2cfe05a04774","role":"sequence","name":"Triangle of B-analogs of Stirling numbers of the second kind.","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-d55b2cfe05a04774","role":"sequence","name":"Triangle of B-analogs of Stirling numbers of the second kind.","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-a65976744dde69f6","claim":"real_rooted"}]}