Finite-Core Signatures in LISA-Band Wave-Optics Lensing by Low-Mass Dark Matter Halos

LISA-band gravitational waves from massive binary black holes can be diffractively lensed by low-mass dark matter halos and subhalos, so their frequency-dependent amplification can probe the inner density profile. We isolate the generic finite-core part of this signal by comparing fixed-mass Navarro-Frenk-White (NFW) and cored-NFW lenses and propagating both profiles to the complex wave-optics amplification factor. A finite core smooths the time-delay response and reshapes the diffraction peak; an NFW template with a lower concentration can mimic part of the effect, but structured complex residuals remain after time and phase alignment. The residual peaks for intermediate cores, r c/r s 0.25 -- 0.3. An SIDM-inspired isothermal-core profile gives the same qualitative response, showing that the signal is not an artifact of one cored parameterization. For a fiducial LISA source, an appreciable mismatch requires favorable near alignment and M vir 10 7M. The result is a finite-core baseline for isolated line-of-sight halos and for subhalos perturbing strongly lensed macro-images.