Journey Operators for Structured Multi-Axis Composition

תקציר מקורי באנגליתarXiv:2607.26775v1 Announce Type: cross Abstract: Many kinds of data have structure along one or more axes: words in a sentence, pixels in an image, nodes in a tree, frames in audio, or cells in a 3D volume. Along one axis, order matters: "the dog bit the man" is different from "the man bit the dog." Across independent axes, however, neither composition nor movement should depend on the order of axes: in an image, composing right then down should give the same result as composing down then right, and moving right then down should describe the same relative position as moving down then right. We develop a framework for modeling this kind of multi-axis structure. Each data item carries its content together with a small transformation for each axis. A path connecting two positions defines a j