Object-centric video models represent scenes with slots, yet exposed geometry can vary in meaning with appearance. In Invariant Slot Attention (ISA), explicit position and scale can disagree with the decoded center and extent; edits can yield unexpected motion or resizing, and replacing appearance can shift geometry. GeoCo-SAVi promotes geometric authority and semantic alignment. Its spatially equivariant, object-wise decoder makes position and scale effective commands: changing them moves or resizes the rendered support. Factual position alignment ties position to the decoded center, and normalized attention overlap discourages duplicate allocation. Appearance transplantation aligns geometry semantics across objects, so recipient geometry governs layout while donor appearance supplies shape. A temporal initializer propagates calibrated slots across frames. On Obj3D, GeoCo-SAVi matches ISA reconstruction, reduces p-centroid error by over 80%, and cuts appearance-induced size variation by over 50% while producing the expected translation and scale responses. On 250 MOVi-C videos, it also improves reconstruction, instance grouping, and fixed-identity geometry control over two same-protocol references. GeoCo-SAVi transforms explicit geometry into compositional control, making both position and scale more readable and editable.

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