{"id":"e-f91a02f39edc297f","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-765f9e2b013b3c68","premise_count":0,"theorem":"polytool parent provers, route periodic_product: every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"49ad6f78935d5d19ece4b9e22dfddac41dbb74adca3538fd4eeb719ac9a4597c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":629,"certificate_compressed_size":375,"conclusion_name":"Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical letters (1 <= k <= n).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-765f9e2b013b3c68","claim":"one_signed_coefficients"},{"node_id":"n-765f9e2b013b3c68","claim":"hadamard_kernel"},{"node_id":"n-765f9e2b013b3c68","claim":"real_rooted"}]}