{"id":"e-bd5b203c620a1609","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-fac4d4a000d744e8","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":"ed16a15de1e00b5e0affa8c72a0de3120afd9c37a3aa9a6f2dc97c140642ddb5","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13757,"certificate_compressed_size":2629,"conclusion_name":"Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros).","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-6758fe7729845be8","role":"sequence","name":"Triangular array binomial(2*n-k, k), k=0..n, n >= 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-fac4d4a000d744e8","claim":"one_signed_coefficients"},{"node_id":"n-fac4d4a000d744e8","claim":"hadamard_kernel"},{"node_id":"n-fac4d4a000d744e8","claim":"interlacing"},{"node_id":"n-fac4d4a000d744e8","claim":"real_rooted"}]}