{"id":"e-20a66a93533ac8e0","operation":{"map":"A038255","operation":"basis_map"},"operation_detail":"A038255","conclusion_id":"n-c72653d9ab0ee8be","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":"5c3a9da4ffcc2a29cc3994efd23e9cbf604b0c73a70c87623dd7d64c52c8d68c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":12056,"certificate_compressed_size":2311,"conclusion_name":"Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-cc04537b3d998791","role":"sequence","name":"basis-map coefficients of Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1.","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"6"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 6]"}],"cited_by":[{"node_id":"n-c72653d9ab0ee8be","claim":"one_signed_coefficients"},{"node_id":"n-c72653d9ab0ee8be","claim":"hadamard_kernel"},{"node_id":"n-c72653d9ab0ee8be","claim":"real_rooted"}]}