Integral cohomology of dual boundary complexes is motivic

In this note, we give a motivic characterization of the integral cohomology of dual boundary complexes of smooth quasi-projective complex algebraic varieties. As a corollary, the dual boundary complex of any stably affine space (of positive dimension) is contractible. In a separate paper [Su23], this corollary has been used by the author in his proof of the weak geometric P=W conjecture for very generic $GL_n(\mathbb{C})$-character varieties over any punctured Riemann surfaces.
Comment: 8 pages; Following the anonymous referee's suggestion, the original paper arXiv:2307.16657 (v3) has been separated into two: v4 of that paper keeps the main result; this one deals with the motivic part