{"id":"e-fa5fc5a793cceca0","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-6234241a3daf2f61","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":"0aa47b17a19925bd50c7b4524d064ea391912f742dc82a5140a6a66ef22719ad","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":9442,"certificate_compressed_size":2510,"conclusion_name":"obreschkoff_combination of Coefficient triangle for polynomials used for e.g.f.s for unsigned Stirling1 diagonals.","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-a36b2e24b7a3dbb7","role":"sequence","name":"Coefficient triangle for polynomials used for e.g.f.s for unsigned Stirling1 diagonals.","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-a36b2e24b7a3dbb7","role":"sequence","name":"Coefficient triangle for polynomials used for e.g.f.s for unsigned Stirling1 diagonals.","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-6234241a3daf2f61","claim":"real_rooted"}]}