After nearly a year on the market and a dramatic series of price reductions, the Woolworth Mansion on East 80th Street — Manhattan’s largest private residence— has entered into contract, The Post has learned. Records show the property entered contract on Oct. 27. The final sale price and the identity of the new owner have not yet been disclosed.  The 20,000-square-foot limestone mansion, designed in 1915 by C.P.H. Gilbert for retail magnate Frank Woolworth’s daughter Helena, was most recently