{"id":"e-22417f5eeaa55b57","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-bfcfc0c48e00f4c8","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":"0ecc7a23bbb25968c46cf1ffc033d837526fd94d483a89a6f4588d2348e9440d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13674,"certificate_compressed_size":2721,"conclusion_name":"shift_x_plus_one of basis-map coefficients of Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ed81f100961f7473","role":"sequence","name":"basis-map coefficients of Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n).","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-bfcfc0c48e00f4c8","claim":"one_signed_coefficients"},{"node_id":"n-bfcfc0c48e00f4c8","claim":"hadamard_kernel"},{"node_id":"n-bfcfc0c48e00f4c8","claim":"real_rooted"}]}