{"id":"e-4ea38c3ef421f3f7","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-9f660947dd0578ca","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":"423525845232e861cd6cf80a3623f6a582d65a37b82c57deb5adc42bcb04aaf6","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":10542,"certificate_compressed_size":2793,"conclusion_name":"obreschkoff_combination of Triangle of coefficients of (x+1)*(x+3)*(x+6)*...*(x+n(n+1)/2).","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-ecd77b030b8fab94","role":"sequence","name":"Triangle of coefficients of (x+1)*(x+3)*(x+6)*...*(x+n(n+1)/2).","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-ecd77b030b8fab94","role":"sequence","name":"Triangle of coefficients of (x+1)*(x+3)*(x+6)*...*(x+n(n+1)/2).","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-9f660947dd0578ca","claim":"real_rooted"}]}