{"id":"e-9d50a926c8b79db7","operation":{"map":"A027467","operation":"basis_map"},"operation_detail":"A027467","conclusion_id":"n-c27b11147fce8bfa","premise_count":1,"theorem":"geometric family P_k = g(t) (a + d t)^k: T(p) = g(t) p(a + d t), so the roots of T(p) are those of g and the points (r - a)/d for the roots r of p (elementary)","lean_route":null,"lean_declarations":[],"certificate_hash":"5646c7d892f4ca1e3a24dc82f4c693fcbefc3c014c25d758fa2c15605d4ea1d0","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14372,"certificate_compressed_size":2760,"conclusion_name":"Riordan array (1+2x,x(1+x)).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-8be1ba22f08cce79","role":"sequence","name":"basis-map coefficients of Riordan array (1+2x,x(1+x)).","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"15"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 15]"}],"cited_by":[{"node_id":"n-c27b11147fce8bfa","claim":"one_signed_coefficients"},{"node_id":"n-c27b11147fce8bfa","claim":"hadamard_kernel"},{"node_id":"n-c27b11147fce8bfa","claim":"real_rooted"},{"node_id":"n-c27b11147fce8bfa","claim":"interlacing"}]}