{"id":"e-b91bf4c52fd06745","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-146f1cd501c36740","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":"0dbc7353cbaae390847a6d29468844e253dc4966f8f5a8500bb862b8dbbeb295","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6897,"certificate_compressed_size":1401,"conclusion_name":"basis_map_A013611 of basis-map coefficients of A scaled Hermite triangle.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-5fe240122e98ffb3","role":"sequence","name":"basis-map coefficients of A scaled Hermite triangle.","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-146f1cd501c36740","claim":"real_rooted"},{"node_id":"n-146f1cd501c36740","claim":"one_signed_coefficients"},{"node_id":"n-146f1cd501c36740","claim":"hadamard_kernel"}]}