{"id":"e-45d2c5cd5b9739d8","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-492f384fe03c9268","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":"07263578592f12feba64533ee9438fd657f451b6403736f9ee20d6b8435bf18e","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1588,"certificate_compressed_size":738,"conclusion_name":"row_factor parent of Triangle read by rows: T(n,k), for k=-n..n-1, is the scaled (by 2^n n!) probability that the sum of n uniform [-1, 1] variables is between k and k+1.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-492f384fe03c9268","claim":"one_signed_coefficients"},{"node_id":"n-492f384fe03c9268","claim":"hadamard_kernel"},{"node_id":"n-492f384fe03c9268","claim":"real_rooted"}]}