{"kind":"parent_provers","proof":{"attempts":[{"detail":"c and the seeds are nonzero, real-rooted and of one sign, so P_(n0 + k m + i) = c^m P_(n0 + i) is too","route":"periodic_product","success":true,"variant":"P_(n+k) = c(x) P_n"}],"conditional_on":[],"route":"periodic_product","rows_checked":10,"statement":"every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","status":"proved"},"record":{"first_index":0,"initial_polynomials":[["1"]],"recurrence":{"terms":[{"coeff":{"coeffs":[["0","-1"]]},"deriv_order":0,"offset":1,"sign":"none"}]},"schema":"polytool.recurrence.v1"},"try_root_domain":true}