Published September 12, 2025 | Version v1 Publication Open 1. Independent Researcher Description The operational primitives of deep learning, primarily matrix multiplication and convolution, existas a fragmented landscape of highly specialized tools. This paper introduces the Generalized WindowedOperation (GWO), a theoretical framework that unifies these operations by decomposing them into threeorthogonal components: Path, defining operational locality; Shape, defining geometric structure andund...