arXiv:2610.32890v1 Announce Type: new Abstract: While multimodal contrastive models like CLIP and CLAP successfully learn shared representations, their embeddings typically exhibit a persistent \emph{modality gap}. We propose addressing this separation through a purely geometric approach: changing the embedding domain from the unit sphere, $S^{d-1}$, to the probability simplex, $\Delta^{d-1}$. Although both manifolds share the same intrinsic dimension, the simplex acts as a structural prior; its nonnegative, unit-mass constraints serve as a cross-modal calibration that forces both modalities to ground themselves in the same coordinate system. By attaching lightweight softmax adapters and using Total Variation similarity, we reduce the centroid $\ell_2$ gap by 97--99\% across five multimodal retrieval benchmarks. This confirms that simplicial geometry induces genuine semantic alignment, matching or exceeding the retrieval performance of standard unconstrained models.