{"id":"e-cf6c2292b090b00e","operation":{"operation":"parent_provers","route":"paper_theorem"},"operation_detail":"paper_theorem","conclusion_id":"n-c8b3f39d03de798f","premise_count":0,"theorem":"polytool parent provers, route paper_theorem: every parent row P_n, n >= 1, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"814c4ca297798907dfc9f319136fe7fd9af7893ae816aa0fe168eef86b54b6db","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":2298,"certificate_compressed_size":976,"conclusion_name":"Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by upward antidiagonals.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-c8b3f39d03de798f","claim":"real_rooted"},{"node_id":"n-c8b3f39d03de798f","claim":"one_signed_coefficients"},{"node_id":"n-c8b3f39d03de798f","claim":"hadamard_kernel"},{"node_id":"n-c8b3f39d03de798f","claim":"interlacing"}]}