Distance as an Informational State: A Non-Metric Foundation of Spatial Emergence

Classical physics fundamentally treats distance, length, and spatial extension as axiomatic geometric quantities, considered independent of underlying informational processes. This paper challenges this paradigm and introduces an alternative, information-first ontology: distance is not a geometric axiom but an emergent informational state resulting from the minimal path length of a relational information process. Within this framework, space is fundamentally relational, time represents a discrete update order of operations, and entropy manifests as divergence pressure within an underlying informational graph. Furthermore, cosmic expansion is modeled as the growth of graph complexity, while black holes are defined as compression nodes that cause path lengths to collapse. By replacing geometric spacetime with an information-based dynamic, this model bridges quantum foundations, relational physics, and discrete computer science, offering a novel class of synthetic physical architectures that are both theoretically compatible and algorithmically implementable.