  We demonstrate the effectiveness of one of the many multi-tracer analyses
enabled by Optimal Transport (OT) reconstruction. Leveraging a semi-discrete OT
algorithm, we determine the displacements between initial and observed
positions of biased tracers and the remaining matter field. With only
redshift-space distorted final positions of biased tracers and a simple premise
for the remaining mass distribution as input, OT solves the displacement field.
This extracted field, assuming asymptotically uniform density and a gradient
flow displacement, enables reconstruction of the initial overdensity
fluctuation field. We show that the divergence of the OT displacement field is
a good proxy of the linear density field, even though the method never assumes
the linear theory growth. Additionally, this divergence field can be combined
with the reconstructed protohalos to provide a higher signal-to-noise
measurement of the BAO standard ruler than was possible with either measurement
individually.
