{"id":"e-b160bf4cdac48f45","operation":{"operation":"parent_provers","route":"paper_theorem"},"operation_detail":"paper_theorem","conclusion_id":"n-c914b69838ac70ec","premise_count":0,"theorem":"polytool parent provers, route paper_theorem: every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"d02d73e48688558b5334bf46704849a4ced982dfea3a73cb59520d6c47805373","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":2198,"certificate_compressed_size":912,"conclusion_name":"Triangle read by rows: row n consists of the nonzero coefficients of the expansion of 2^n x^n in terms of Hermite polynomials with decreasing subscripts.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-c914b69838ac70ec","claim":"one_signed_coefficients"},{"node_id":"n-c914b69838ac70ec","claim":"hadamard_kernel"},{"node_id":"n-c914b69838ac70ec","claim":"interlacing"},{"node_id":"n-c914b69838ac70ec","claim":"real_rooted"}]}