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an exact degree step keeps every row nonzero; here S_n is the identity; with lag L = 2, the induction runs in each residue class of n modulo L from its start row","lean_route":null,"lean_declarations":[],"certificate_hash":"30520bf1367cead70b82c551497edb2f2ec1797ae00f476fec2dda7f2af61606","verification_polytool":"replayed","verification_lean":"not_attempted","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[]},"premises":[]},{"edge":{"id":"e-35a33ce2a6b89415","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-35bd700768cac55f","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":"13aa8470d7a29a8e69823a43535a961ed830ec2f97e8d7b9f4a5eeb46f233efa","verification_polytool":"replayed","verification_lean":"not_attempted","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[]},"premises":[]}]}]}]}]}],"truncated":false,"expanded":4}