Dark matter imprints on a caustic encounter in an effective spinning black hole binary lens

Abstract

We ask whether a cored dark matter (DM) correction can leave a resolved caustic trace after a spinning vacuum binary is allowed to imitate it. The vacuum comparison varies lens scale, common spin, separation, mass ratio, projected spin angle, and one phase offset fitted over the full orbit. Nearby unequal component spins and projected directions are also tested. The best high-resolution fit remains the equal-mass, common-spin model. In the selected encounter, the local root mean square residual is $1.34\times10^{-2}$, the maximum residual is $4.02\times10^{-2}$, and the aligned crossing shift is $1.51\times10^{-3}$. A nearby resolution gives $1.50\times10^{-2}$, $4.02\times10^{-2}$, and $1.82\times10^{-3}$. All three rising half-response crossings are checked, and the selected event is not the largest. This is a numerical demonstration within a tested effective family, not an observational claim or an exact binary-spacetime calculation.