{"id":"e-ffc8a9fffd6e96cb","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-efd1fdf07e5468d8","premise_count":0,"theorem":"polytool parent provers, route root_domain: every parent row P_n, n >= 1, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"f84973ed4fdf84037270ad3e602b8891ad5adabe00cb17bc8c4663844af9e172","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":2221,"certificate_compressed_size":827,"conclusion_name":"Euler's triangle: triangle of Eulerian numbers T(n,k) (n>=0, 0 <= k <= n) read by rows.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-efd1fdf07e5468d8","claim":"one_signed_coefficients"},{"node_id":"n-efd1fdf07e5468d8","claim":"hadamard_kernel"},{"node_id":"n-efd1fdf07e5468d8","claim":"real_rooted"}]}
