Bijection conjecture for mixed and bordered-mixed complexes

A finitely generated mixed complex is a mixed complex of the form used in the paper with finite generation understood in the source, and a bordered-mixed complex is a tuple $C=(C_1,C_2,\rho)$ where $C_1$ is a $\mathbb F[U,V,V^{-1}]$-complex, $C_2$ is a type $D$ structure over the bordered algebra of the torus, and $\rho$ is a $\mathbb F[V,V^{-1}]$-homotopy equivalence. Consider these objects up to weak equivalence. Bijection conjecture for mixed and bordered-mixed complexes. Finitely-generated mixed complexes up to weak equivalence and bordered-mixed complexes up to weak equivalence are in natural bijection. The conjecture asserts that the bordered and unbordered mixed-complex descriptions encode equivalent classification data; no resolution is supplied in the source.