Discrete Relational Network Dynamics (DRND): A Fully Emergent Framework for Spacetime, Matter, and the Evolution of Fundamental Constants

Abstract: Contemporary cosmology exhibits persistent internal tensions, including discrepancies in late- and early-Universe inferences of the Hubble parameter and open questions surrounding the physical origin of the Dark Sector. Most extensions of the concordance model modify the stress-energy content while retaining a smooth background manifold and fixed fundamental constants. Here we outline Discrete Relational Network Dynamics (DRND), a background-independent framework in which spacetime, matter degrees of freedom, and effective dynamical laws emerge from an evolving discrete graph of causal relations. Dimensionality is treated as a dynamical, scale- and environment-dependent property characterized by the network's spectral dimension dS defined via diffusion on the graph. Within a minimal toy description based on random-walk transport, we propose that the effective signal-propagation speed c_eff can depend on the network topology, with high-connectivity phases (large dS) enabling faster causal processing and low-connectivity/percolative regimes (reduced dS) inducing longer traversal times. We discuss a phenomenological parameterization in which c_eff(z) modifies cosmological distance measures and can mimic part of the phenomenology usually attributed to Dark Energy under the assumption of constant c. We also formulate a qualitative screening picture in which virialized regions remain effectively three-dimensional (dS ≈ 3), suppressing local detectability. The paper is intended as a framework and a set of falsifiable directions, and we explicitly separate heuristic scaling relations from future work required for full dynamical consistency and data fitting (SNe, BAO, CMB).