{"id":"e-c0733b4d3f559bd0","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-8229dbdd6a4b5cd9","premise_count":0,"theorem":"polytool parent provers, route root_domain: every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"758b0a38786772cbfcbb447a5d9a3a16ecb021b3e76bd8863c21c898d7aa8821","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1159,"certificate_compressed_size":609,"conclusion_name":"Triangle read by rows, s_3(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-8229dbdd6a4b5cd9","claim":"one_signed_coefficients"},{"node_id":"n-8229dbdd6a4b5cd9","claim":"hadamard_kernel"},{"node_id":"n-8229dbdd6a4b5cd9","claim":"real_rooted"}]}