We prove a two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener–Hopf operators with discontinuous symbols. The discontinuities occur on surfaces which are assumed to be piece-wise smooth. Such a two-term formula was conjectured by H. Widom (On a Class of Integral Operators with Discontinuous Symbol, Toeplitz centennial (Tel Aviv, 1981), pp. 477–500. Operator Theory: Advances and Applications, vol. 4. Birkhäuser, Basel, 1982), and proved by A. V. Sobolev for smooth surfaces in 2009 (Mem. AMS 222(1043), 2013)
