Foundations of the REST Framework: The Relational Emergence of Spacetime

The continuous spacetime manifold is widely treated as the fundamental arena of physical reality. This paper challenges that assumption, proposing that spacetime is not an ontological foundation, but rather an emergent macroscopic bookkeeping artifact—dispensing with the background continuum much like the elimination of the luminiferous aether in the 20th century. We introduce the Relational Emergence of SpaceTime (REST), a rigorously background-independent framework that constructs physical reality exclusively from discrete, asynchronous bipartite graph combinatorics. By defining the fundamental unit of interaction as a topological closed loop (the "both-way handshake"), we establish a strict hierarchy where local proper time emerges as an interaction tick-count, and spatial dimensions arise from relative coupling frequencies. From this purely combinatorial base, standard physics is entirely recovered and recontextualized. We demonstrate that the Schrödinger equation emerges as the infinitesimal diffusion limit of network path-counting, while the Minkowski metric and Lorentz invariance are derived as the necessary algebraic rules to maintain logical consistency among asynchronous observers. Furthermore, Spin-1/2 is organically derived as the topological reconciliation ratio of the directed bipartite network. Extending the framework to macroscopic information geometry, the Einstein Field Equations are recovered via the Cramér-Rao bound and Fisher information as the thermodynamic equation of state of the relational graph. Crucially, embedding the chiral asymmetry of the weak interaction into this network reveals a fundamental topological frustration. This generates a strict geometric noise floor that analytically derives the empirical MOND acceleration scale (a_0 \approx 1.2 \times 10^{-10} \text{ m/s}^2) from first principles. Ultimately, the REST framework demonstrates that reformulating physics without a pre-existing spacetime container yields a deterministic, unified origin for both quantum kinematics and relativistic gravity, without violating their core principles.