Tissue tearing degrades optimal-transport and diffeomorphic registration of spatial transcriptomics beyond displacement magnitude: a multi-seed deformation benchmark and a supervised graph cross-attention proof-of-concept.

Background. Three-dimensional reconstruction from serial spatial-transcriptomics (ST) sections requires registering adjacent slices, but physical sectioning introduces tears -- discontinuous, non-isometric deformations. Leading methods rely on priors that tears strain: PASTE/PASTE2 use Fused Gromov-Wasserstein optimal transport (OT), which assumes near-isometric preservation of within-slice distances, while STalign and CODA use diffeomorphic (LDDMM) mapping, which cannot change tissue topology. Learned-deformation ST methods are emerging (STaCker, INST-Align), but OT/diffeomorphic behaviour under tearing has not been systematically characterised. Methods. On the spatialLIBD human DLPFC Visium dataset (Maynard et al., 2021; 3 donors), we build a controlled benchmark -- known smooth warps, single-block rigid tears (expression unchanged), and an identity self-control -- at severities of 0-8 spot pitches, scored against an approximate array-position ground truth (~8 px residual). We evaluate three unsupervised incumbents -- PASTE2 (OT, over five warp seeds), STalign (diffeomorphic LDDMM), and GPSA (Gaussian-process warp) -- add a magnitude-matched smooth control, and test a minimal graph model, Sutura (per-slice graph encoder -> cross-attention correspondence -> per-spot displacement; spatial coupling is local kNN message passing only, no explicit smoothness penalty). Sutura is trained supervised on each tissue's ground truth; all baselines are unsupervised. Generalisation is assessed by leave-one-donor-out across all three donors. Results. OT registration is robust to smooth warps but degrades reproducibly under tearing: nearest-correspondence (argmax) error 722 +/- 5 -> 855 +/- 27 px and layer accuracy 64.9% -> 60.5% (mean +/- 95% CI, 5 seeds). The effect is not merely displacement magnitude: at a matched mean displacement (~2000 px), a smooth warp costs 769 px / 60.2% accuracy whereas a tear costs 863 px / 57.5% -- an extra ~100 px and ~3 points attributable to the discontinuity. STalign (LDDMM) and GPSA (GP warp) both collapse at severe tears (866 px and 931 px respectively), confirming tear-collapse is field-wide across three independent method families. Trained and evaluated on the same donor, Sutura fits torn-tissue correspondence to a median 99 -> 106 px (5-seed), but under leave-one-donor-out is 1236 +/- 2 -> 1584 +/- 52 px -- approximately 1.8-3.6x worse than PASTE2 on every unseen donor. A contrastive correspondence loss halves the gap on two of three donors (to 816 -> 949 and 749 -> 826 px, approximately 1.1-1.2x PASTE2 at worst-case tear) but is modest on the third and never surpasses PASTE2. Conclusion. Tearing is a real, magnitude-controlled failure mode of all three incumbent method classes. A learned model fits it in-sample but donor-invariant generalisation remains open. The contrastive fix roughly halves the held-out gap on two of three donors and nears PASTE2 at worst-case tear, but does not surpass it: donor-invariance is improved, not solved. The durable contribution is the benchmark, the characterisation across three method families, and an honest negative with a diagnosed mechanism.