From Pre-Geometric Coherence to the Present Universe: Planck-Scale Step Count, Horizon, and Age in the Sobolev–Ozok–Lattice Framework

This paper extends the Sobolev–Ozok Lattice (SOL) framework to cosmology and argues that the Universe is far older than conventionally inferred. In SOL, spacetime is a discrete coherence lattice at the Planck scale. A single structural quantity—the residual vacuum coherence fraction, set by surface-to-volume scaling of lattice domains—determines the total number of causal “steps” since the onset of cosmic coherence. From this step-count picture, the model yields a cosmic horizon of about 46.7 billion light-years and a corresponding coherence age of about 46.7 billion years.

The result stands in contrast to the 13.8-billion-year age inferred within the standard ΛCDM framework. In this work, the standard age is interpreted as a model-dependent projection that arises when a fundamentally discrete evolution is forced into a continuous FRW description. By treating discreteness as primary and continuity as emergent, the SOL approach replaces multi-parameter density fits with a single geometric scaling.

The framework is falsifiable. It predicts specific, observable departures from ΛCDM: suppressed and aligned large-scale CMB modes, small phase offsets in baryon acoustic oscillations, slight achromatic delays in fast radio bursts, and systematic mismatches between gravitational-wave and electromagnetic luminosity distances. Together, these signatures provide a direct empirical path to confirm or refute the SOL cosmology and its central claim of an older Universe grounded in first-principles lattice coherence.