A Scale-Relative Model of SpaceTime

We present a scale-relative model of spacetime in which geometry and topology are primaryentities, evolving continuously with observational scale. Unlike conventional frameworks that treatmass, time, or energy as fundamental, this approach generates structure, forces, and matter from theintrinsic evolution of geometry and topology of spacetime across resolution domains. Two functionsgovern this evolution: a smearing function describing geometric coarse-graining, and a bandwidthfunction capturing the scale-limited information accessible to an observer. Topological degrees offreedom exist in superposition, encoded in a scale-dependent Betti number function reflecting theprobabilistic presence of bulk features. Bulk bends induce conformal phase transitions on boundary-like surfaces, reorganisingentanglement and spectral structures as geometric degrees of freedom emerge or vanish. Thisgeneralises AdS/CFT into a Topology/CFT duality, where superposed bulk topologies correspond tosets of boundary conformal structures. The Scale Flow Equation (SFE) governs the joint evolutionof geometry and topology, whose non-trivial dynamics naturally select three spatial dimensions.Each scale domain exhibits characteristic symmetries and emergent forces via Noether’s theorem.Gravity and the arrow of time arise from scale-dependent symmetry breaking, while matter andmass originate from resistance to topological flow. By placing scale-dependent geometry and topology at the foundation, this framework provides aconceptually minimal yet physically rich perspective, offering new avenues to understand the originof spacetime, quantum gravitational phenomena, and the emergence of fundamental interactions.