{"id":"e-34b0075c2d0a2285","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-2baae9820c5a4b1e","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":"36c31a049e7ec63dfd5122cd9bbe385304446d3cb41d1cb5ff507899fd8e56e9","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":10353,"certificate_compressed_size":2551,"conclusion_name":"obreschkoff_combination of Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-cb5d49e71e46f2ed","role":"sequence","name":"Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).","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-cb5d49e71e46f2ed","role":"sequence","name":"Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).","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-2baae9820c5a4b1e","claim":"real_rooted"}]}