{"id":"e-6ef42593efb6357c","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-1e156f12069736a3","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":"2a2599c65c17bb7af737a12c3f6bde42e073d3a852fef4461b1eb9bb0b1e22f0","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6865,"certificate_compressed_size":1391,"conclusion_name":"basis_map_A013611 of basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-74c1e94669ff21ff","role":"sequence","name":"basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-1e156f12069736a3","claim":"real_rooted"},{"node_id":"n-1e156f12069736a3","claim":"one_signed_coefficients"},{"node_id":"n-1e156f12069736a3","claim":"hadamard_kernel"}]}