Cosmic Clepsydra: A Unified Framework of Spacetime, Matter, and the Universe

Abstract We present Cosmic Clepsydra, a unified framework in which the structure of spacetime, the properties of matter, and the behavior of the universe on cosmological scales are all derived from a single geometric construction: a network of N = 3 fibers per point, fully connected by a complete graph K3, on which stochastic fluctuations produce two inseparable imprints—a discrete tick (time) and a local twist (mass). From this single structure, without introducing additional axioms beyond those stated in §2, we derive the following results. (Microscopic): the emergence of continuous time from statistically averaged discrete ticks (§3); a Lagrangian formulation with fixed coupling ratios (§5–6); the topological stability of matter as paired helical configurations (“twin dance” Hopfions, §7); vanishing strong-CP angle θ = 0 as a direct consequence of the left– right symmetry of the network (§8); the Berry sign σ = ±1 distinguishing fermions from bosons (§9); and the three-generation mass hierarchy with the absence of a fourth generation, enforced by N− 1 = 2 as the maximum allowed twist count (§10). (Macroscopic): infrared gravitational screening and a dark-energy-like accel- erated expansion as geometric consequences of the spider-web tension reaching its stretching limit (§11); dark matter as topological knots confined to a subset of the N = 3 layers, invisible to light yet gravitationally coupled through the K3 full-connectivity (§12). (Unifying prediction): the fundamental frequency K0 and the Hubble con- stant H0 are connected through the network size √N via K0 = H0√N , linking microphysics (strong-interaction scale) to cosmology (cosmic expansion) without introducing free parameters (§13). This relation is observationally testable and offers a new perspective on the Hubble tension. The framework introduces no free parameters beyond those already present in the Standard Model and general relativity, and a single geometric motif—the spider web through which fluctuations pass to become time and matter—unifies all results presented. Keywords: fiber bundle, phase coherence, Hopfion, topological mass hierarchy, dark matter, dark energy, Hubble tension.