Discretum Theory

Context The prevailing standard cosmological model faces fundamental challenges in explaining the key observational phenomena concerning the physical nature of dark matter and dark energy, the small-scale core-cusp problem, and the Hubble tension. Although successful on large cosmological scales, the model's core reliance on non-baryonic cold dark matter particles and the cosmological constant lacks any direct non-gravitational experimental evidence to date, while also exhibiting significant systematic discrepancies on small scales. Core Problem How can one construct a self-consistent theoretical framework—without introducing unknown particles or additional ad hoc parameters—that not only fully explains all gravitational phenomena from galactic to cosmological scales and remains compatible with the verified results of both General Relativity and Quantum Mechanics, but also makes explicit predictions directly testable by next-generation experiments? My Approach and Theory This paper systematically develops the Discretum Theory. Taking a globally continuous and indivisible universe-state as the physical substrate and establishing its covariant mathematical formalism through four core axioms, the theory derives the emergent dynamics from discrete sequential evolution to continuous spacetime. The theory contains only one core free parameter, with all other cosmological parameters being derived quantities. In the weak-field, low-velocity limit, the theory naturally reduces to the linear approximation of General Relativity. Under long-wavelength, slowly-varying conditions, its statistical structure aligns with the core principles of Quantum Mechanics. Furthermore, through the topological features of structural attributes, it naturally connects with the three gauge interactions of the particle physics Standard Model. Main Conclusions and Significance This theory successfully performs joint fits to multiple sets of cosmological observational data, including galaxy rotation curves and the cosmic microwave background radiation power spectrum. The fitting performance is highly compatible with the standard cosmological model within reasonable statistical bounds, and the parameter constraints are consistent with established astronomical observational benchmarks. The Discretum Theory puts forward several quantitatively testable predictions. By providing a unified emergent explanation for the problems of dark matter and dark energy without introducing new particles, it also offers a self-consistent theoretical framework for addressing small-scale cosmological puzzles.