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Fold a leading transform inside the image scope as cm followed by the local transform; an enclosing transform uses the opposite multiplication order. This preserves the complete requested image and crop displacement under an outer scale. The exact crop-arrange-group-move fixture previously moved only five points for a ten-point request; saved geometry and rasters now match an independent direct Transform control across both axes and signed offsets. Full scoped Linux native, wasm and repository gates pass. Co-Authored-By: Codex GPT-6.1 <noreply@openai.com>