Step 1: Picture a cut through one half of the spinal cord. The deficits sort themselves by where each tract crosses the midline.
Step 2: Position sense, vibration and discriminative touch travel up the posterior (dorsal) columns and stay on the entering side until they decussate high up in the medulla. Because the lesion sits below that crossing point, these modalities drop out on the side of the lesion, i.e. ipsilaterally.
Step 3: Pain and temperature behave differently. Their second-order neurons cross almost immediately in the spinal cord, so a hemisection knocks them out on the contralateral side, not the same side. That removes $Pain$ and $Temperature$ as same-side answers.
Step 4: Touch is partly carried by both pathways and is not the classic same-side loss tested here. The clean ipsilateral loss is proprioception.
\[\boxed{\text{Proprioception}}\]